The hosts had already sealed a series success thanks to Spencer Johnson's five-for in Saturday's second match, and any hopes Pakistan had of taking a consolation win were dashed by a dismal performance with the bat in Hobart.
Pakistan were bundled out for just 117 as Aaron Hardie finished with figures of 3-21 and Johnson (2-24) and Adam Zampa (2-11) also dismissed two apiece for Australia.
Babar Azam's knock had put Pakistan in a decent position at 61-1 through six overs, but when Haseebullah Khan handed Matthew Short a simple catch off Zampa's spin ball, the wickets began to tumble with ease.
Pakistan's next five wickets fell for just 31 further runs, with seven of their batters finishing in single figures and four managing one run or fewer, with Babar (41) the only batter to score above 30.
Australia lost Short and Jake Fraser-McGurk early but Marcus Stoinis took any jeopardy out of the chase by scoring an unbeaten 61 runs off 27 balls, with his stand including five fours and five maximums.
Stoinis was unwilling to hang around, smashing Haris Rauf for 22 runs in an over to take Australia to the brink.
He then hit Shaheen Shah Afridi for 19 in the penultimate over as the hosts got the job done with 52 balls remaining.
Data Debrief: Quick and easy for Stoinis
Australia could have taken their time after being set such a paltry target, but Stoinis was determined to put on a show for those present at the Bellerive Oval.
Only twice has he bettered his knock of 61 in T20Is – versus New Zealand in 2021 (78) and against Oman at the World Cup earlier this year (67*). His strike rate of 225.92, while ruthless, falls some way short of his T20I best of 327.77 versus Sri Lanka in 2022 (59 off 18).
Pakistan's Babar, meanwhile, is now second on the all-time list of T20I run scorers with 4,192 to his name, having overtaken Virat Kohli. Only Rohit Sharma (4,231) is ahead of him.
Australia captain Finch sustained a knee injury during the final game of the T20 series with the West Indies in Saint Lucia – the tourists suffering a 4-1 defeat.
The 34-year-old, who suffered a cartilage problem earlier in the series, has subsequently missed the opening two one-day internationals between the nations at the Kensington Oval.
After the final ODI on Monday, Justin Langer's side travel to Bangladesh for another five-game T20 series as they step up preparations for the World Cup in October.
Finch, who scored a T20I record of 172 runs against Zimbabwe in July 2018, is likely to undergo surgery on his right knee upon returning to Melbourne.
And although frustrated to be departing the tour, the skipper is confident it will increase his chances of leading Australia out in three months' time.
“I’m extremely disappointed to be heading home,” he said.
“This was considered the best course of action rather than heading to Bangladesh, not being able to play and losing that recovery time.
“I will have surgery if required and start the recovery process ahead of the World Cup."
Taking place in Oman and the United Arab Emirates, the T20 World Cup will run from October 17 to November 14.
Australia have been drawn alongside the Windies in Group 1 of the Super 12 stage, as well as England and South Africa.
Runners-up to England in 2010, Australia will be seeking a first triumph in the event, which they are also set to host next year.
In a lopsided encounter remarkably similar to the first of the three games between the teams, the tourists posted a challenging total before skittling their opponents.
Opening duo David Warner and Aaron Finch both made half-centuries as they powered Australia to 193-5 after being put into bat.
The Proteas – who managed just 89 when chasing 197 last Friday – lost captain Quinton de Kock early and never threatened in a reply that lasted just 15.3 overs.
Mitchell Starc claimed the key early breakthrough, bowling left-hander De Kock with the fourth ball of the innings, and also removed Faf du Plessis cheaply during the powerplay. The paceman finished with figures of 3-23, wrapping up the win by trapping Kagiso Rabada in front.
Ashton Agar also claimed three wickets, with the spinner coming close to recording a second hat-trick in the series after seeing off Anrich Nortje and Lungi Ngidi with successive deliveries in the 15th over.
Tabraiz Shamsi survived to deny Agar another treble but South Africa did not last too much longer, bowled out for 96 – the lowest total posted in a T20I at the Cape Town venue.
They appeared set to be chasing well in excess of 200 when Warner (57) and Finch (55) were in full flow, the pair putting on 120 in 11.3 overs.
Australia rather lost their way after the well-set pair departed in quick succession, yet Steve Smith – who surprisingly came in down at number five in the order – benefited from a repreive when bowled by a Rabada no ball to make an unbeaten 30 in a hurry.
Starc's double strike had South Africa teetering and while Rassie van der Dussen (24) and Heinrich Klaasen (22) tried to repair the damage, the slow-bowling combination of Agar (3-16) and Adam Zampa (2-10) turned the screw. Fittingly, the impressive Starc landed the knockout blow.
The two teams now turn their focus to 50-over cricket with a three-match ODI series rounding out Australia's trip. The first match takes place in Paarl on Saturday.
At the Wanderers in Johannesburg, left-arm spinner Agar was the unlikely chief destroyer as he finished with figures of 5-24 in a 107-run victory.
Australia made 196-6 before bowling out South Africa for a meagre 89 in the first of three matches between the teams in the shortest format.
Agar reduced South Africa from 44-4 to 44-7, and incredibly he almost took a second hat-trick later in the innings, only narrowly missing out on bowling last man Tabraiz Shamsi after taking wickets at the end of the 12th and start of the 14th over.
"It was really exciting, obviously a highlight of my cricketing life," Agar said at the post-match presentation, where he was named man of the match.
"But my job's made a lot easier when I've got Mitch Starc, Patty Cummins, Richo [Kane Richardson] and Zamps [Adam Zampa] doing the job before me."
Agar revealed he was not at his best before the match began, but thrashing 20 not out from nine balls at the end of Australia's innings must have set him right.
"It's funny, I was actually feeling horrible leading into the game," Agar said.
The man from Melbourne found it difficult to explain why the day proved such a personal success.
Trying to pin it down, he said: "I don't know... that self-belief at the top of the mark, to just let it all out and give it your best go.
"Obviously when the wicket turns a bit, you get a bit of assistance, your job gets a bit easier and you get on a roll and keep going."
Agar saluted captain Aaron Finch for the brilliant slip catch that clinched the hat-trick, removing Dale Steyn after the spinner earlier prised out Faf du Plessis and Andile Phehlukwayo to tease the big chance.
Finch appeared more thrilled than Agar as he charged off in celebration.
"Unbelievable catch, I think he really enjoyed it as well," Agar said. "He was halfway off the ground when I looked over.
"But great catch, great team performance, good game."
The 29-year-old suffered the problem when fielding at mid off as she attempted to run out New Zealand captain Sophie Devine during Australia's four-run win.
Perry immediately went to the ground clutching her right hamstring and a scan on Monday revealed a high-grade tear that will rule her out of Australia's semi-final on Thursday and, should they progress, Sunday's final.
It is a huge blow to Australia given Perry's status as the number one all-rounder in T20 cricket, a position she shares with Devine in the ICC rankings.
"She's obviously been a massive part of our squad and our team for a long time," Australia captain Meg Lanning had said of Perry after the win over New Zealand.
"You can't replace her, but we've got 15 players here who can do a job and you need a squad to win the World Cup."
Top spot was on the line at the Rose Bowl, after England twice beat Aaron Finch's side to make sure they would win the series. This third and final game presented a chance for England to swipe away Australia's proud world-leading status, but the tourists raised their game to protect that position.
Rashid's 3-21, including a glorious googly that outfoxed Finch, almost turned the match England's way, but their attack was blunted once his allocation was used up, and the tourists stayed calm to get the job done.
Mitchell Marsh made his highest T20 international score - 39 not out - to guide Australia beyond England's 145-6, his chancy single off Chris Jordan securing the win with three balls to spare.
It means Australia remain premiers in the International Cricket Council's T20 standings, albeit with England perched right behind them.
Tom Banton was promoted to the top of the England order in the absence of Jos Buttler, with Moeen Ali captaining the side for the first time with Eoin Morgan ruled out by a finger injury.
Australia put England in, and the reshuffling got off to a worrying start when Banton fell for two to Josh Hazlewood.
Opening partner Jonny Bairstow made a brisk 55, Dawid Malan added 21, Moeen chipped in with 23, and Joe Denly contributed 29 not out, but England's total always looked on the low side and proved to be so.
Moeen was given out after a moment of uncertainty, as he clubbed Mitchell Starc towards the deep midwicket boundary where Steve Smith, with his left foot devilishly close to the boundary, held on.
Australia were 86-2 in 10 overs, looking for all the world comfortable, having lost only Matthew Wade (14) and Marcus Stoinis (26) to that point.
Yet Rashid had the tourists rattled when he took two wickets in three balls, nicking out Glenn Maxwell and Finch, the latter removed for 39 by a dream of a delivery that befuddled the Australia skipper.
The Yorkshire leg-spinner took his third wicket from the final ball of his permitted four overs, having Smith caught and bowled for three.
Marsh had crucially survived a scare between Rashid's second and third wickets, when he edged Denly towards Malan at slip and the England fielder missed the chance.
Australia needed 46 from 42 balls after Rashid's stint, with five wickets standing and Marsh and Ashton Agar at the crease.
England swapped spin for pace by summoning Jofra Archer and Mark Wood, and it was a change of tack that Australia welcomed, Marsh pulling Wood for six from the first ball of the 16th over.
The Australians gathered 14 runs from that over, thoroughly calming their nerves, and it was steady all the way to the finish line from there.
The Black Caps restricted Australia to 142-8 from their 20 overs after the visitors won the toss and elected to bat in Wellington, with Ish Sodhi taking 3-24.
Guptill (71 from 46 balls) eased any anxiety about a smaller run chase on a pitch being used for the third time this series, with New Zealand claiming victory with 27 balls to spare.
New Zealand's successful chase bucked the series trend of the side batting first winning every game.
Australia captain Aaron Finch said: "We probably just weren't aggressive enough with the bat. We probably let them dictate slightly, but we didn't get enough runs and kept losing wickets at regular intervals.
"A couple of us put a fair bit of time into our innings, 20, 30, 40 balls and then to not go on with that it was probably the difference in the game. If one of us gets 60 or 70, that might be a 160-170 score and then you're a couple of good power-play overs away from really squeezing."
Sodhi was named as the player of the series, finishing with 13 wickets at an average of 12.07 across five games.
The win was set up by a disciplined bowling display led by Sodhi, while Trent Boult (2-26 with 10 dot balls) did early damage, Mitchell Santner (0-21 with 10 dots) was tight and Tim Southee (2-38 with eight dots) restricted Australia at the death.
Boult trapped Josh Philippe lbw early before Finch (36 from 32 balls) and Matthew Wade (44 from 29 balls) put together a 66-run second-wicket stand.
Finch, who came under pressure earlier in the series after a poor run of form on the back of the Big Bash League, managed one six and five fours during his knock, while Wade hit two maximums and three fours.
Sodhi got the breakthrough with Finch slicing to Santner at point, leaving Australia 74-2 after 10 overs before the innings fell away, with Glenn Maxwell falling for one, Ashton Agar for six and Mitchell Marsh for 10.
Australia lost 68-6 in the final 10, including being restricted to 36-4 from the last five overs, battling an inconsistent pitch and tight New Zealand bowling.
Devon Conway (36 from 28) and Guptill combined for a 106-run opening partnership in the chase, before Glenn Phillips (34 not out from 16) finished the job.
Guptill blasted four sixes and seven fours in his knock, going at a strike rate of 154.35.
Riley Meredith (2-39) took two wickets in two balls, with Conway caught in the deep by Agar and Kane Williamson trapped lbw for a golden duck, but it was too little, too late.
The defeat compounds a bad 24 hours for the Aussies, after India's Test win over England on Saturday confirmed Australia would miss the Test Championship final.
Black Caps captain Williamson said: "Incredibly hard-fought series and momentum shifts throughout. Then to finish with three games on a surface, try and get a read on it was a real challenge."
The 36-year-old called it quits in ODIs last September, but continued to captain Australia later in the year in the T20 format as they looked to defend their World Cup title on home soil.
However, Finch's side failed to reach the semi-finals despite the right-handed batsman top-scoring in a group-stage victory over Ireland, one that ultimately ended up being his last international match.
Finch has called it a day after a fantastic international career, during which he set the record for the highest score in a T20I with his 172-run innings against Zimbabwe in 2018.
He played for Australia 254 times across the three formats with 146 ODIs and 103 T20Is, as well as five Test matches.
Finch will continue playing for Melbourne Renegades in the Big Bash League after racking up 3,120 T20I runs, putting him sixth in the all-time rankings.
Finch told reporters at the MCG: "Realising that I won’t be playing on until the next T20 World Cup in 2024, now is the right moment to step down and give the team time to plan and build towards that event.
"I also want to say a huge thank you to all the fans who have supported me throughout my international career."
Finch captained his country in 76 T20Is and 55 ODIs, with his finest hour as Australia skipper coming in 2021 when he led them to the T20 World Cup, while he was also part of the team that won the 50-over Cricket World Cup in 2015.
Finch added: "Team success is what you play the game for and the maiden T20 World Cup win in 2021 and lifting the ODI World Cup on home soil in 2015 will be the two memories I cherish the most.
"To be able to represent Australia for 12 years and play with and against some of the greatest players of all time has been an incredible honour."
A crowd of 86,174 – a record for a women's cricket match – witnessed the tournament hosts dominate throughout at the famous MCG.
Australia posted 184-4 after opting to bat first, Mooney top-scoring with an unbeaten 78 from 54 deliveries.
However, it was opening partner Healy who stole the show, capitalising on an early life - she was dropped by Shafali Verma in the first over - to hit the fastest half-century in an ICC final.
Watched by husband Mitchell Starc, who was given permission to leave Australia's tour of South Africa early to be at the game, Healy needed just 39 balls to smash 75.
The right-hander hit seven fours and five sixes - including three in a row during an over from Shikha Pandey - before she was eventually caught at long on, ending a first-wicket stand worth 115 with Mooney.
Chasing such a daunting target, India stumbled out of the blocks. The big-hitting Verma fell to the third ball of their reply, caught behind by wicketkeeper Healy off the bowling of Megan Schutt.
Taniya Bhatia had to retire hurt due to concussion before Jemimah Rodrigues was caught at mid on, leaving the score at 8-2 at the end of the second over.
Deepti Sharma was the only player to provide any real resistance with 33, Schutt finishing with figures of 4-18 as India were bowled out for 99 with five balls remaining.
Despite the absences of Tayla Vlaeminck and Ellyse Perry, who both suffered injuries in the group stage, Australia were crowned T20 champions for a fifth time, albeit this is their first title on home soil.
The Pakistan Cricket Board (PCB) confirmed details of a month-long tour in March and April 2022 comprising three Test matches, three ODIs and one T20I.
The Tests will be held in Karachi, Rawalpindi and Lahore in March, with the latter also hosting the white-ball matches.
While the Tests will form part of the ICC World Test Championship, the one-day matches will be linked to the ICC Cricket World Cup Super League, a 13-team event from which seven qualifiers and host nation India will progress to the final tournament in 2023.
Speaking of Australia's first visit since 1998, PCB chairman Ramiz Raja said: "I am delighted to welcome Australia to Pakistan. From a personal point of view, it pleases me no end that we'll be engaged in a three-Test match series, connoisseurs delight.
"Australia are one of the high-performing sides and them playing in our backyard for the first time after a gap of 24 years will be a special treat for the fans.
"Likewise, it will be a great opportunity for the Australia cricketers to not only play at our iconic venues but also feel and enjoy the respect, love and hospitality that this great country offers, something which most of their previous generation of cricketers missed out by playing offshore."
Cricket Australia chief executive Nick Hockley: "Cricket Australia is excited about the prospect of touring Pakistan next year for what will be a highly anticipated series in a country so incredibly passionate about the game and their national team.
"Pakistan is a formidable opposition with an exceptionally talented team, as evidenced by their dynamic performances in the current ICC Men's T20 World Cup in the UAE.
"We thank the PCB for their considerable efforts in planning for the tour and look forward to continuing to work closely over the coming months to finalise the necessary operations, logistics, security and Covid-19 protocols.
"The safety and welfare of our players and staff remains our number one priority, and we will continue to work with the PCB and relevant agencies to ensure that appropriate and sufficient arrangements are put in place for the tour."
Australia won the series 1-0 in their previous tour of Pakistan, which was their first since Richie Benaud's side won 2-0 in 1959-60.
The previous four series between the countries have been held offshore, most recently in 2018-19, when Pakistan won 1-0 in the United Arab Emirates.
The 37-year-old will complete his stage-by-stage international retirement at the conclusion of the tournament, where Australia begin their campaign against Oman on Thursday.
The reigning Cricket World Cup winners and World Test champions, who will also play England, Scotland and Namibia in Group B, are aiming to complete the sweep of global international honours in the United States and West Indies.
Warner would be one of four players to have appeared in all three finals, along with Mitchell Starc, Pat Cummins and Travis Head.
A steady and injury-hit Indian Premier League season with the Delhi Capitals - led by three-time World Cup winner Ponting - led to question marks over his selection for this competition.
But, to Ponting, Warner's inclusion was never in doubt, and he is backing Jake Fraser-McGurk - the winner of the IPL's 2024 Electric Striker of the Season award and a travelling reserve - to fill the void when he brings the curtain down on his international career.
"He's the sort of character you want to have around your team, especially in big tournaments like World Cups," Ponting told ESPNcricinfo.
"He's just one of those natural winners. Everything he does, he wants to win. You can see that with his attitude in the field and the way he goes about his cricket.
"There's more than just the runs that we'll be missing when Warner finally is gone. But hopefully, the depth of Australian cricket is good enough to find someone to come in and fill that void."
"It's going to be a really big set of shoes to fill, there's no doubt about that. They have got a lot of depth there.
"I'd be very surprised if he [Fraser-McGurk] doesn't go straight into the T20 team when David's finally done. I was lucky enough to coach him at the Delhi Capitals this year as well. He's got extreme talent."
Axar played a massive part in India's 3-1 Test series victory over England earlier this year, taking 27 wickets at an average of 10.59 in three matches.
The 27-year-old has now gone into isolation, having contracted COVID-19 after arriving at the Capitals' team hotel.
"Delhi Capitals all-rounder Axar Patel has tested positive for COVID-19. He had checked into the team hotel in Mumbai on March 28, 2021, with a negative report. His report from the second COVID test, came positive," Delhi announced in a statement on Saturday.
"He is currently in isolation at a designated medical care facility. The Delhi Capitals medical team is in constant touch with Axar and ensuring his safety and well-being. We wish him a speedy recovery."
The Capitals face Chennai Super Kings in their first match of the tournament at the Wankhede Stadium next Saturday.
The Amazon Warriors won the toss and opted to field first. The decision went in their favour when they restricted the Knight Riders to 45-2 at the end of the PowerPlay. However, despite taking regular wickets the Knight Riders had several useful cameos throughout their innings to post a challenging 173 to win.
The Amazon Warriors timed their chase perfectly in reply and had an excellent partnership between Ayub and Hope to thank as the two batters scored half centuries to lay the foundation for the Amazon Warriors power hitters to seal the victory at the death.
In the first innings, the Knight Riders got off to a bad start losing Mark Deyal and Nicholas Pooran in the PowerPlay, the latter falling to a tremendous one-handed catch from wicket keeper Azam Khan.
When Martin Guptil skied one off the bowling of Imran Tahir to leave the Knight Riders on 57-3, the innings needed rebuilding.
Akeal Hosein and Lorcan Tucker stepped up to task the and put the Knight Riders back in the game before Tucker was run out for 38 off 25 balls.
Andre Russell kept the momentum up by hitting a couple of Republic Bank maximums before he departed for a quick-fire 14. His dismissal brought Kieron Pollard to the wicket and the captain responded with a brutal 25 from 12 balls, however, like those before him he failed to kick on.
Ultimately the innings was underpinned by Akeal Hosein. His unbeaten 44 helping to guide the Knight Riders to a competitive score of 172-8.
Much like the Knight Riders, the Amazon Warriors were to get their innings off to an inauspicious start. Chandrapaul Hemraj falling inside the first two overs for 10.
However, Ayub and Hope went on to lay the foundation for the Amazon Warriors chase with a brilliantly constructed partnership of 93 from 67 balls.
Despite Ayub (62) and Hope (51) eventually falling at the back end of the innings. Azam Khan and Shimron Hetmyer hit several Republic Bank maximums to seal the win in style.
The victory means the Amazon Warriors return to the top of the 2023 Republic Bank Caribbean Premier League (CPL) table.
Scores: Guyana Amazon Warriors 175-4 (Ayub 62, Hope 51; Russell 2-29, Khan 2-30) beat Trinbago Knight Riders 172-8 (Hosein 44*, Tucker 38; Smith 3-31, Paul 1-17) by six wickets
The Shaheens concluded their run in the competition with a three-wicket triumph over Ireland in Florida on Sunday, but failed to progress to the Super 8 stage at the expense of the United States.
Shaheen Afridi starred for Pakistan by taking three wickets, with Azam leading from the front with the bat as he hit an unbeaten 32 to help secure the victory.
"Yes we finished well, we took early wickets with the ball," Azam said after the game. "With the bat we didn't finish well. Lost back to back wickets, got over the line in the end.
"I think with the bowling, conditions suit our bowlers, in batting few mistakes in USA, India matches, when you lose wickets pressure is on you.
"Let's see, what team needs, I'll be okay with it. Have a good bunch of players, we've to go home, chat and see where we lacked, and then come back. Couldn't finish off close games, as a team we weren't good as a team."
Pakistan's exit from the World Cup was the earliest they had been knocked out of the competition, having lost their opening two games to the USA and India.
Azam's future as the captain has been called into question, and could hand the armband over to Afridi, who was named as the new captain following Pakistan's league stage exit of the ODI World Cup in India last year.
The 29-year-old explained that conversations will be had to discuss his future as Pakistan captain, but admitted the decision is down to the PCB.
"When I left captaincy (previously), I felt that I shouldn't be captain any more and announced it myself. When PCB gave it back, that was their decision," Azam said.
"Now we'll go back and have a discussion about what all has happened here. If I leave captaincy again then I will inform everyone.
"For now, I haven't thought about it and the decision is up to PCB."
Pakistan claimed a five-wicket victory in the opening game in Lahore on Friday, and Babar and Hafeez ensured the hosts were in cruise control again at the same venue on Saturday.
After Bangladesh finished on 136-6 thanks predominantly to Tamim Iqbal's 65, Babar (66 not out) and Hafeez (67no) combined superbly for an unbroken stand of 131.
It meant Pakistan clinched the match and the three-match series with 20 balls to spare, rendering Monday's finale a dead rubber.
Bangladesh opener Mohammad Naim went for a duck in the second over and, though Tamim held the innings together, he found little in the way of partners.
Afif Hossain (21), stayed with Tamim for a stand of 45, but after the latter was run out in the 18th over, any impetus Bangladesh's innings had was lost.
Shafiul Islam removed Ahsan Ali for a duck to give Bangladesh hope of defending their total, which was swiftly and brutally extinguished by Babar and Hafeez.
Hafeez brought up his half-century in 39 balls, but Babar was four deliveries quicker, the pair hitting 16 fours and two sixes between them as they tormented the Bangladesh attack en route to an easy win.
Babar called correctly and asked the tourists to bat in Rawalpindi, on a different surface to the one Pakistan prevailed upon when the teams met on Friday.
The outcome was much the same, with Zimbabwe's innings never truly gaining any momentum after Haris Rauf (3-31) removed openers Brendan Taylor and Chamu Chibhabha inside the first four overs.
Leg-spinner Usman Qadir (3-23) was the pick of the Pakistan attack and his double-strike in the 10th over, accounting for Sikandar Raza (seven) and Wesley Madhevere (24) - bowled and lbw respectively by brilliant googlies - left Chibhabha's men 66-5.
From that point it became a matter of occupying the overs, something they managed thanks in large part to Ryan Burl's anchoring and unbeaten 32, which concluded with a six over midwicket off Wahab Riaz as Zimbabwe reached 134-7.
That never looked likely to be enough to contain Pakistan, even when Fakhar Zaman drove Blessing Muzarabani to mid-on in the second over.
That brought Haider together with Babar and they proceeded to compile 100 for the second wicket in 10.3 overs.
Babar raced to 51 off 27 deliveries before departing next ball to Muzarabani (2-33), impressively backing up his match-winning 82 in the series opener.
Haider, who drove with particular panache off the back foot, saw Pakistan home with a minimum of fuss as he finished unbeaten on 66 off 43 deliveries.
The three-match series concludes in Rawalpindi on Tuesday.
Captain Babar made 52 but it was Mohammad Rizwan's unbeaten 91 that powered Pakistan to 165-3 in the third and final game at the Harare Sports Club.
That total proved beyond Zimbabwe, though Wesley Madhevere (59) had the hosts in contention. They were 102-1 at one stage in reply, only to lose three wickets for eight runs to scupper their hopes.
Tadiwanashe Marumani departed for 35 to trigger the mini collapse and, despite 20 from Brendan Taylor, the innings fell away in the closing stages, finishing up at 141-7 to lose by 24 runs.
Hasan Ali was the star performer for Pakistan with the ball, taking career-best figures of 4-18, as the tourists bounced back after a first ever loss to Zimbabwe in the format on Friday.
With his side bowled out for 99 when chasing in the previous game, Babar opted to bat first after winning the toss. Sharjeel Khan fell for 18 in the powerplay but the skipper combined with opener Rizwan to put on a crucial second-wicket stand worth 126.
The partnership eventually came to an end when Babar was caught in the deep in the final over, with Fakhar Zaman then falling immediately in similar fashion as he registered a first-ball duck.
Luke Jongwe benefited from the late double to finish with figures of 3-37, giving him nine wickets in the series at an average of 8.77. He had claimed 4-18 in his team's victory but the hosts were unable to pull off a repeat result.
The two nations now switch their focus to Test cricket. A two-match series begins in Harare on Thursday.
Rizwan gets maximum rewards
As was the case in the opening fixture, the home team appeared in a strong position in a run chase, only to falter as the finishing line drew into sight. Madhevere hit seven of his team's 16 fours, yet they did not manage a solitary six between them.
Indeed, Rizwan was the only player to clear the boundary rope in the match, doing so three times as he registered a fourth unbeaten half-century in his past seven T20 games.
Captain fantastic in fine form
The ever-consistent Babar has now managed 50 or more on 11 occasions in T20 cricket for Pakistan since the start of 2019, a fine run of form that has helped him reach a notable personal milestone.
He made it to the 2,000-run mark in 52 innings - four fewer than India skipper Virat Kohli. His career average in the format now stands at a hugely impressive 47.32.
Andy Balbirnie's 77 helped Ireland to their first victory over Pakistan in this format on Friday, but Babar's side responded in style on Sunday with their own seven-wicket triumph.
Lorcan Tucker's 51 powered Ireland to an impressive 193-7 in Dublin as Shaheen Shah Afridi registered figures of 3-49 and Abbas Afridi managed 2-33.
Yet that total was far from imposing as Pakistan chased the target down with 19 balls to spare thanks to a remarkable partnership between Mohammad Rizwan and Fakhar Zaman.
The pair combined for a 140-run stand off only 78 balls for the third wicket as Fakhar smashed 78 from 40, while Rizwan was unbeaten on 75 after facing just 46.
"I'm relieved, credit to all batters," Babar said after the win. "We lost a few wickets early on but we kept the momentum going.
"Fakhar is very experienced and played according to situation which demanded positive intent. It's a good side, we got positives in this match and will look to give 100 per cent in the next match."
Rizwan added: "They played really well against us. It was not an easy chase because the Ireland bowlers knew their conditions better.
"They gave us a difficult time early on, but we decided that chasing 194, we have to attack. You're always under pressure when you lose especially with World Cup around the corner."
The two sides will meet again in Dublin on Tuesday to settle the three-match T20I series.
Wesley Madhevere top-scored with 70 as Zimbabwe posted 156-6, having opted to bat first in Rawalpindi on Saturday.
However, Babar - who sits second in the International Cricket Council's T20 batting rankings - made sure the hosts had few issues in their chase, hitting 82 from 55 balls at the top of the order.
The Pakistan skipper managed nine fours and a solitary six as he put on 80 for the third wicket with Mohammad Hafeez - who made 36 - following the dismissals of Fakhar Zaman (19) and Haider Ali (7)
Blessing Muzarabani - Zimbabwe's hero as they won the third and final ODI on Wednesday following a Super Over - dismissed both well-set batsmen, but Pakistan still cruised home with seven deliveries to spare.
Haris Rauf and Wahab Riaz earlier claimed two wickets apiece as the tourists slipped to 87-4 after Brendan Taylor won the toss.
Madhevere led the rebuild thanks to a career-best knock in the format, while Elton Chigumbura - who has announced he will retire at the end of the tour - added 21 in a hurry during the closing overs.
Zimbabwe will look to stay alive in the three-match series when the teams meet again at the same venue on Sunday.
Babar hit 69 runs off 44 balls before being bowled by Ben Sears, smashing six fours and two sixes to take his team to 123/3 at the time of his dismissal.
Fakhar Zaman (43 from 33) and Usman Khan (31 off 24) also chipped in with important innings as Pakistan ended on 178/5.
With a target of 179 to secure a 3-1 series victory, New Zealand's run chase faltered almost immediately as opener Tom Blundell was removed within the first over with his team having managed just five runs on the board.
Blundell's fellow opener Tim Seifert steadied the ship with a vital 52-run innings off 33 deliveries before being bowled by Usama Mir, but Shaheen Shah Afridi led the way for Pakistan, finishing with figures of 4-30 to stem the New Zealand run chase
Josh Clarkson's 38 off 26 set up a nervy conclusion, but Pakistan held on to avoid defeat in the T20 series as the teams share the spoils at two wins apiece after the first game was abandoned.
