Babar's side were defeated in the first meeting with Ireland last week but responded with two convincing chases to secure a 2-1 triumph.
Ireland captain Lorcan Tucker's 73 helped his side to set a target of 179 in the winner-takes-all-decider, but Pakistan had little trouble in easing to a six-wicket victory with 18 balls to spare.
Rizwan, who managed an unbeaten 75 in the second meeting, crafted a well-made 56, while Babar carried Pakistan to within touching distance after his 42-ball 75.
Big-hitter Azam Khan blasted 18 off just six deliveries to see the visitors over the line, though Afridi was quick to credit the work of the two experienced Pakistan campaigners.
"For us, before the World Cup, it's important to have these games to ready ourselves and there are a few areas to improve," said Afridi, who impressed with 3-14 in the first innings.
"They're both world-class players [Babar and Rizwan]; they know how to play their role and they have done really well on this pitch."
Babar bludgeoned four of his five sixes off Ben White's bowling in the 14th over, while sharing 139 runs with the in-form Rizwan for the second wicket.
"We had good communication in the middle because we have played a lot of cricket together; we were trying to play on our strengths and the aim was to match with the run rate," Babar added.
"Lots of positives for us to take and we were able to execute our plans.
"We have a big tournament coming up and this is good practice; we are now looking forward to the England series."
Mark Adair was the only Ireland bowler to impress with his economical 3-28, though Tucker was still satisfied with his side's efforts.
"It was brilliant and a great privilege to captain," Tucker said at the post-match presentation. "It would have been nice to start with a win.
"We set up a platform nicely but unfortunately, we couldn't finish well. We gave everyone a go with the ball. Credit to the lads, they bowled well in tough conditions.
"Maybe it was a bit disappointing with the result but we had positives from the series."
The Tallawahs won the toss and opted to field first and they produced a disciplined bowling performance to ensure the Amazon Warriors were restricted to 182/6. Azam Khan produced the star knock in the Amazon Warriors innings, his 54 at the back-end propelling Guyana to a competitive total.
The chase was always going to be a steep one for the Tallawahs and that equation became all the harder when they lost four wickets in the PowerPlay.
It was a position they never recovered from eventually succumbing to 101 all out.
The Amazon Warriors made a solid start in their batting PowerPlay, reaching 49 for the loss of one wicket. It could have been two but for the faintest of inside edges that saved Shai Hope from being dismissed lbw.
However, Saim Ayub departed for 20 immediately following the end of the PowerPlay, his miscued shot only finding Alex Hales at long on.
Hope and Shimron Hetmyer struggled to add some attacking impetus to the innings but just when it seemed they were ready to accelerate Hope was caught on the boundary for 40.
Hetmyer followed shortly afterwards for 31 – but Romario Shepherd and Azam Khan cashed in at the back end. Khan smashed a brutal 54 runs off 27 balls to give the Amazon Warriors momentum heading into the second half of the game.
If the Tallawahs were to chase the 183 to win, they needed a lightning start in the PowerPlay but they got the opposite of that.
Four wickets fell in the first six overs and the procession continued after the fielding restrictions had been lifted. All of the Guyanese bowlers got in on the act to ensure the Tallawahs were never in the contest.
Imad Wasim added a respectable unbeaten 43 but no one stayed with him as the Tallawahs were eventually bowled out for 101.
The Amazon Warriors victory means they will now contest their sixth Republic Bank CPL final where they will aim to win their first ever title.
Making his first England appearance in over a year, paceman Archer dismissed Azam Khan and Imad Wasim as Pakistan were bowled out for 160 while chasing 184.
England captain Jos Buttler was the star of the show in Birmingham, plundering 84 off 54 balls to set the tone for the hosts' innings.
Will Jacks chipped in with a useful 37 before he, like Buttler, was caught out by Shadab Khan from Haris Rauf's bowling.
Shaheen Shah Afridi (3-36) stopped Jonny Bairstow, Moeen Ali or Chris Jordan from getting going, but Archer came in to hit a four and a six to get England to 183-7.
Pakistan were two down within four overs of their chase, and after Babar Azam (32) and Fakhar Zaman (45) were dismissed by Moeen and Liam Livingstone respectively, their chances looked increasingly slim.
Having taken out Azam, Archer (2-28) ended Wasim's stand at 22, with Reece Topley (3-41) and Jordan (1-31) finishing the job for England.
The series now moves to Cardiff, with the final match taking place at The Oval on Thursday.
Data Debrief: Buttler at his best
Buttler may well have to miss part of the upcoming T20 World Cup due to the birth of his third child, and England will be hoping their skipper makes a swift return to action if that is indeed the case.
His knock, which included eight fours and three sixes, marked the second-highest score by an England captain in a T20I, behind Eoin Morgan's 91 against New Zealand in 2019.
Balbirnie plundered 77 from 55 balls, including 10 fours and two sixes, and his partnership of 76 with Harry Tector (36) edged Ireland closer to victory.
Curtis Campher (15*) and Gareth Delany (10*) saw them over the line to secure the win with one ball to spare.
Despite an early setback, Pakistan started strong, with Babar Azam hitting 57 and Saim Ayub adding 45.
However, Craig Young’s strong performance saw him take 2-27 as Ireland took control to limit the visitors in the later stages as Azam Khan and Shadab Khan both walked without getting any runs.
The sides will meet again at the Dublin venue on Sunday and Tuesday.
Data Debrief:
Ireland achieved their target of 183 against Pakistan successfully today, making it their highest run chase against a full-member side in men's T20Is.
Ireland's first win against Pakistan came at the 2007 World Cup and 17 years later they secured a first victory over them in T20 cricket.
Barbados Royals had won the toss and chose to bat, with Rahkeem Cornwall and Kyle Mayers getting them off to a blistering start, combining to score 63 runs in the powerplay. However, Fabian Allen would remove both openers to bring the Tallawahs back into the game, before Azam Khan would continue his fine form with the bat to take the Royals to 161-7.
In response, Brandon King and Shamarh Brooks would produce an 86-run partnership that frustrated the Royals' bowling attack. Despite Jason Holder taking the wicket of Brooks, King would lead the rest of the chase as he scored a magnificent 83 runs from 50 balls to see the franchise win their third Hero CPL title.
Barbados Royals had chosen to bat with the aim of setting an imposing total, Cornwall and Mayers combining well to build an excellent foundation. Once Allen had removed them both with his spin bowling, the run rate slowed down as the Tallawahs wrestled back control of the game. However, Khan, who came in at number three, would bat until the 19th over, scoring his second successive half-century to help the Royals reach 161-7 after 20 overs.
Jamaica Tallawahs suffered an early setback in their chase as opener Kennar Lewis lost his wicket for a duck, but King and Brooks would rebuild at a steady run rate.
Once Brooks lost his wicket in the 11th over, King would shoulder the responsibility of finishing the chase, hitting 15 boundaries in total. In the end, King would take his side to victory with a six, sparking celebrations from Jamaica Tallawahs players, staff and fans.
Scores: Jamaica Tallawahs 162-2 (King 83*, Brooks 47; Mayers 1-14, Holder 1-14) beat Barbados Royals 161-7 (Khan 51, Cornwall 36; Allen 3-24, Gordon 3-33) by 8 wickets.
St Kitts & Nevis Patriots won the toss and chose to field first, with the Royals getting off to a subdued start, reaching 55-2 after 10 overs before a superb 102-run partnership between Azam Khan and Harry Tector propelled them to 156-3 after 20 overs. In their chase, the Patriots got off to a confident start with Andre Fletcher and Evin Lewis building a platform but faltered as the wickets tumbled in the final five overs to leave them 120 all out after 20 overs, losing by 36 runs.
Barbados Royals, who have already secured a place in next week’s playoffs, got off to a very cautious start in their innings, losing openers Rahkeem Cornwall and captain Kyle Mayers in the first eight overs. Sheldon Cottrell, returning to the Patriots' side, led by example in the early overs with a disciplined performance. Yet Khan and Tector revived the Royals innings with some fantastic shot-making that helped reap 95 runs in the final eight overs to take the Royals to 156-3.
St Kitts & Nevis Patriots had got off to a positive start, Fletcher and Lewis navigating their way through the PowerPlay, before Mujeeb ur Rahman took both wickets. The Patriots never found consistency after that, losing seven wickets in the final five overs of the game, as Mujeeb found support from Nyeem Young, who also took three wickets.
The win means Barbados Royals continue their excellent form this season while the Patriots are outside the play-off spots with one game left to play.
Scores: Barbados Royals 156-3 (Khan 64, Tector 47*; Dananjaya 1-25, Jansen 1-32) beat St Kitts and Nevis Patriots 120 all out (Lewis 41, Brevis 21; Young 3-5, Mujeeb 3-18) by 36 runs.
