Despite their rocky start out in the field, England are firmly back in the contest thanks to Root and Harry Brook.
Root started the day on 32, picking up alongside Zak Crawley, with England at 96-1 as they began the long chase.
It looked like it might stall as Crawley was caught by Aamir Jamal for 78, but Ben Duckett (84), who was okay to bat despite injuring his thumb yesterday, steadied the ship once again.
Root made history with a sublime drive for a four, before then bringing up his 35th Test century as he batted through the intense heat to reach 176 not out.
When Jamal pinned Duckett for lbw, Brook arrived with his own century, getting 141 as England pushed to finish the day at 492-3, now only trailing Pakistan by 64 runs.
The tourists have never conceded as many as Pakistan's 556 and gone on to take a first-innings lead, but they have put themselves in a position to do just that on day four.
Data Debrief: History maker
Going into this Test, Root needed just 71 runs to overtake Alastair Cook's all-time record of 12,472, but he more than surpassed that.
At the end of day three, he is now on 12,578 in 147 matches, batting in 268 innings in total. His highest score in that time came against Pakistan (254), while his tally of 176 not out is his highest tally in the host country.
Root now has 35 centuries and struck 1,355 fours and 44 sixes.
Root has enjoyed a brilliant 2022, posting his fourth red-ball international century of the year against New Zealand in the second Test.
It took Root just 116 balls to reach three figures at Trent Bridge, the fewest he has ever scored a century in his Test career, and he has now converted 10 of his last 14 fifties into 100s (71 per cent).
The Yorkshire batter would go on to make 176 in the first innings, hitting 26 fours – the most recorded in an innings by an English batter since Zak Crawley hit 34 in his 267 versus Pakistan in 2020.
That helped England to an unassailable 2-0 series lead over the World Test champions New Zealand, after Jonny Bairstow scored the second-fastest red-ball century for his country on Tuesday.
Root's second century of the series came after his heroics at Lord's, in which he passed 10,000 Test runs with a majestic unbeaten 115, his first fourth-innings international hundred.
The 31-year-old, who stepped down from captaining England in April, has been rewarded with top spot in the world Test batting rankings as he reached the summit for the first time since December 2021.
Labuschagne has dropped down to second, with Australia team-mate Steve Smith in third, while Pakistan captain Babar Azam and New Zealand skipper Kane Williamson make up the top five.
Black Caps number five Daryl Mitchell has also enjoyed a big rise up the rankings after his 190 and 69 not out in the second Test against England, jumping from 50th to 17th.
Meanwhile, in the bowling ratings Australia captain Pat Cummins remains top ahead of India's Ravichandran Ashwin, whose team-mate Jasprit Bumrah is in third.
That is due to Kyle Jamieson dropping three places down to sixth, with Pakistan quick Shaheen Afridi and South Africa star Kagiso Rabada moving up a place to fourth and fifth respectively.
England ended day three of the first Test needing just three wickets to bring the hosts' first innings to a close, with Babar Azam's side on 499-7, still 158 runs behind.
Having laboured to stop Pakistan from chipping away at their lead, England struck late through Will Jacks, James Anderson and Ollie Robinson, taking four wickets in just over 20 overs.
But it was footage of Root rubbing the ball over Leach's head during the day that caught the eye of spectators and now the former captain has spoken out on his strange tactic.
"You've got to get some moisture in it somehow, some weight to try to get it to move around on a placid wicket like that," he stated.
"A nice sweaty, bald head like Jack's is perfect for it. You can see it sat there on his head. He's more than just a pretty face Jack, he is very useful in lots of ways."
Leach, a folk hero among England fans for his role in their famed Headingley comeback against Australia in 2019, has posted figures of 2-160 from 42 overs so far in Rawalpindi.
Despite the cost however, his efforts helped lay the platform for his side's closing flurry, with Root hopeful they can push on over the final two days.
"All the hard work we put in, we got our just rewards," he added. "We had to be quite creative, try to do things differently and think outside the box."
The 33-year-old surpassed Cook's previous high of 12,472 on day three of the first Test against Pakistan on Wednesday.
Root reached the mark by piling on 71 runs in the blistering Multan heat and reached 176 not out at the end of play with England 492-3.
"I'm obviously proud but still feel there is plenty more left to do, and many more runs left to get," Root is quoted as saying by BBC Sport.
"More than anything, the way we played as a team is what stands out - we've got ourselves back in a really good position."
Root's 12,578 runs consist of 35 centuries, 1,355 fours and 44 sixes, coming across 146 matches.
He is now fifth on the all-time list of run-scorers across all nations, with only Rahul Dravid (13,288), Jacques Kallis (13,289), Ricky Ponting (13,378) and Sachin Tendulkar (15,921) ahead of him.
And with time still on his side age-wise, Cook has backed the man who took his England record to overtake each of those legendary names.
"I would be betting on Root to do it," Cook told Test Match Special. "I don't see Root losing that hunger and ability to keep driving himself forward for the next couple of years.
"He's just this consistent run-scoring machine. There are other geniuses who can play genius innings, but Root is a genius with consistency."
England have never conceded as many as Pakistan's 556 and gone on to take a first-innings lead, but they trail by just 64 runs heading into day four.
"We've still got an opportunity to win the game, which is really exciting," Root added. "Hopefully we can kick on tomorrow."
England will start the third Test at the Rose Bowl on Friday with a 1-0 lead after a frustrating weather-ruined contest at the same venue ended in a draw on Monday.
The tourists have not suffered a series defeat in England in the longest format for a decade, drawing on their previous two visits.
England beat West Indies 2-1 when international cricket returned following a coronavirus-enforced hiatus and with scheduling still to be confirmed in such uncertain times, Root has called on his team-mates to step up again in Southampton.
The England captain said: "My message to the guys was quite simple today, that we don't know when the next time will be that we play Test cricket, so let's make sure we throw everything into this week.
"Let's make sure we leave no stone unturned and we give everything to each other and the badge going into this last game.
"The guys have prepared really well over the last couple of days and I fully expect everyone to give everything over the next five days and give ourselves the best chance of winning the series 2-0."
England have named an unchanged squad for the finale, but Root says the hosts will leave it late to name their final XI.
Asked if spinner Dom Bess could miss out in favour of an all-seam attack, he said: "We've not settled on an 11 yet. It's so hard to tell with that wicket right now, it's obviously been under cover for a large proportion of the last week.
"With finally some sunshine and a bit of wind, it could change drastically over the course of today. Try and keep everything on the table for tomorrow, then we'll make a call."
The two sides agreed to start 30 minutes earlier than scheduled in the final Test if time is lost due to bad weather on the previous day.
England had their backs against the wall for much of last week at Old Trafford but made a remarkable recovery to win the series opener after Chris Woakes and Jos Buttler led a successful 277-run chase.
Root's side are now preparing for the second match against Pakistan at Southampton, where they can clinch the series and the captain can claim a seventh Test win in succession.
Yet Root did not feel he performed his duties particularly effectively in Manchester, although the match moved the team in the right direction.
"I didn't think I had a very good game last week, to be honest," he told reporters. "I made a few errors, tactical errors, but that can happen from time to time.
"You're not always going to get it right. I think most importantly, it's very clear for the guys how we're looking to play.
"Those messages are consistent and we're seeing improvement week in, week out. That's a really promising sign for the group, and long may that continue.
"Most importantly, we're looking forward, it's not about me, it's not about how many games we win with me as captain, it's about us getting consistently better over a long period of time, looking towards being the number one side in the world.
"If we can maintain that attitude collectively, winning obviously breeds confidence all the time. And people putting in performances like Jos and Wizz [Woakes] did on that final day will breed confidence in the rest of the guys, too.
"The other players, young batters in the team, looking at those two getting the job done, will think, 'I want that to be me next time, I want to be the one stood there at the end having won the game when the heat was on'.
"The more and more we can keep performing like that and keep winning, the quicker I think our development as a side will move forward."
As was the case in the host's series-levelling victory at Headingley on Sunday, sweltering conditions and a dry surface played into the hands of the spinners, with Adil Rashid (4-35) again the England attack.
Moeen Ali returned a miserly 1-19 from his four overs as the England seamers went wicketless and Mohammad Rizwan carried his bat for a 57-ball 76 within 154-6.
Jason Roy went six, four and out in Leeds but produced something more substantial here, with 12 fours and a six before perishing on the slog sweep at Usman Qadir for 64 off 36 deliveries.
Jos Buttler (21) and Jonny Bairstow (five) also skewed slow bowling skywards and Eoin Morgan (21) joined an out-of-sorts Dawid Malan with the score 112-4 after 15 overs, Moeen having been cleaned up by Mohammad Hafeez (3-28).
Pakistan skipper Babar Azam went back to pace in a pivotal 18th over and Morgan flogged him for a pair of sixes, although Hasan Ali had the last laugh, having the England captain caught at mid-on with four balls remaining.
Malan's dogged 31 had been ended by Hafeez and Liam Livingstone had gone six and out by that stage, meaning a pair of scampered twos from all-rounder Chris Jordan were required to finish the job.
Zalmi won the toss and elected to field first but were left to regret that decision when Quetta openers Ahsan Ali and Will Smeed put on a massive 155-run partnership for the first wicket before Ali was dismissed for 73 in the 16th over.
Smeed, a 20-year-old Englishman, was eventually dismissed for 97, in the final over, to see the Gladiators finish with a formidable 190-4 off their 20 overs.
Smeed’s 97 came off 62 balls with 11 fours and four sixes.
Pakistani Usman Qadir was the best bowler for Zalmi with 2-20 off his four overs.
Openers Tom Kohler-Cadmore and Yasir Khan put on 43 for the first wicket before Khan was dismissed in the fourth over for 30 off 12 balls.
Kohler-Cadmore was next to go for 22 to leave the Zalmi 62-2.
Jamaica Tallawahs batsman Haider Ali also contributed 19 before the chase was spearheaded by Hussain Talat and captain Shoaib Malik with scores of 52 off 29 balls and 48 not out off 32 balls, respectively.
Rutherford also contributed 10 runs off nine balls to put them on the brink of victory, being dismissed in the final over with three runs to win.
Malik then hit the winning runs to close the innings on 191-5.
Mohammed Nawaz took 3-44 from four overs for the Gladiators.
The 2022 PSL started yesterday with the Multan Sultans beating the Karachi Kings by seven wickets.
The Kings, led by the number-one-ranked T20 batsman in the world Babar Azam, won the toss and chose to field.
Peshawar posted 173-4 off their 20 overs thanks to a top score of 52 not out off 28 balls from Captain Shoaib Malik that included five fours and two sixes.
Afghanistan power hitter Hazratullah Zazai contributed a 27-ball 41 at the top of the innings while Rutherford ended not out on nine from four balls with one six.
Umaid Asif was the best bowler for the Kings with 3-36 from four overs.
Despite a well-compiled 90 not out off 63 balls from Azam, the Kings ended agonizingly short of their target finishing 164-6 off their 20 overs.
Babar’s knock included 12 fours and one six while Englishman Ian Cockbain was the next best contributor with 31 from 19 balls.
Mohammad Umar was the pick of the Zalmi bowlers with 3-22 from his four overs.
Peshawar Zalmi are now fourth in the points table with four points while the Karachi Kings have yet to register a point after registering their fourth loss in as many games.
Having struggled in his previous five innings in England's seven-match T20I series, when managing just 59 runs, Salt hit a blistering 88 not out from 41 deliveries on Friday.
Salt reached a half-century in 19 balls – the third-fastest by an England player in the format – as the tourists levelled up the series at 3-3 in Lahore.
That set up a decider on Sunday, when Salt will have another chance to underline his credentials to retain his spot at the top of the order at the upcoming T20 World Cup.
"I'm very grateful for the backing I've got from my team-mates and the management. It's very clear the way they want me to play," the 26-year-old said.
"The way I play is aggressive and I want to win as many games as possible while I'm in an England shirt.
"The first few games haven't gone to plan – I've been finding ways to get out, hitting fielders or whatever – but it's nice to come up with a performance like that in a big game.
“It's always a challenge at the top of the order when you feel like you're playing well but you're picking out fielders and finding ways to get out.
"It was definitely [my best T20 innings] and it was nice to do it with the series in the balance."
With Jos Buttler due to return from injury in time for the World Cup, Salt is realistically in competition with Alex Hales over partnering the white-ball skipper.
"You need competition. The best sides in the world have competition and you can't get away from that – it's the same in any sport," Salt added.
"Everyone is trying to put their best foot forwards and show the coaching team and the team-mates how good they are.
"I'm not looking too far into the future; I'm just focused on the next game in a couple of days' time."
Salt's destruction of the Pakistan attack came after home captain Babar Azam had hit an unbeaten 87 to set England a target of 170 for victory.
Babar became the first Pakistan batter to reach 3,000 T20I runs during his half-century, doing so in the absence of the rested Mohammad Rizwan.
He is the fifth men's player to reach that milestone in the format and the joint-quickest to do so alongside India great Virat Kohli.
Reflecting on what was ultimately a disappointing day for his side, however, Babar said: "After losing a couple of early wickets, we thought 170 was a good score.
"Maybe we were 10 runs or so short, but the way Salt batted in the first four or five overs, they took the game away from us.
"The way they used the powerplay was the turnaround today. I think the middle-order needs to step up, they need to take responsibility."
Pakistan recovered from a slow start that saw them 15-2 at one point to post 169-6 at the Gaddafi Stadium, thanks in large to the brilliant Babar Azam (87 not out).
But England made easy work of the chase as they reached 100 from seven overs to set up a decider on Sunday.
Without in-form Mohammad Rizwan, Pakistan initially struggled as Mohammad Haris (7) and Shan Masood (0) fell early on, leaving Babar to do much of the leg work.
Haider Ali (18), Iftikhar Ahmed (31) and Asif Ali took their side to 136-4, but the latter upper cut to Reece Topley for nine runs and Mohammad Nawaz (12) followed soon after.
Babar's 87 did at least give England something to think about, but Salt and Alex Hales put on an opening partnership of 55 off 23 balls, before the latter was removed for 27.
Salt reached his half-century off just 19 balls en route to an unbeaten 88, including the decisive shot as England posted 170-2 to level things up.
Babar brilliance not enough
Pakistan were without run machine Rizwan but Babar stepped up with 87 runs off 59 balls, which included three sixes and seven fours.
Babar surpassed a milestone 3,000 T20I runs in the process, yet it was not enough to steer the hosts to an unassailable series lead.
England ease to victory
The tourists were set 170 to avoid a third successive T20I defeat to Pakistan for the first time ever and had no trouble in reaching that target.
Only once before – against New Zealand in November 2019 (6.4 overs in a game reduced by rain to 11 overs) – have England previously reached 100 from seven overs.
Salt played a key part in that as he underlined his credentials to partner Jos Buttler at the upcoming T20 World Cup.
The 36-year-old allrounder has become a popular figure in the country, where he has captained Pakistan Super League (PSL) Peshawar Zalmi to the title. The player has, however, been recognized for an even more important contribution and that is his prominent role in advocating for the return of international cricket to Pakistan.
The country was blacklisted as a destination for international cricket in 2009 after a horrific attack on the Sri Lankan team bus outside the Gaddafi Stadium in Lahore. International cricket, however, returned to the country in 2017, with Test cricket returning last year.
Sammy was the first player to agree to tour Pakistan when the Pakistan Cricket Board (PCB) attempted to bring the PSL final to the country.
When an ICC World XI was lined up to tour Pakistan for three T20Is in September 2017, it was Sammy who spoke as part of that squad to the other tourists as part of a security briefing.
The idea of honourary citizenship was first broached by Javed Afridi, the owner of Peshawar Zalmi. The PCB then followed up with the federal government and the honour was accepted. Sammy will also receive the Nishan-e-Pakistan, the country's top civilian award, on March 23 in Islamabad.
Mitchell Santner's stunning run out sparked the Black Caps, who claimed two late wickets to bowl out Pakistan before stumps and leave the tourists still trailing by 192 runs on Monday.
Pakistan had crawled to 80-6 amid the looming prospect of having to follow on before captain Mohammad Rizwan (71) and Faheem Ashraf (91) shared a 107-run seven-wicket partnership to lead the team to 187-6.
But Rizwan and Pakistan's stubborn resistance was broken by a run out following Santner's direct hit at Bay Oval in Mount Maunganui, where Yasir Shah (four) was the next to go before Kyle Jamieson (3-35) and Neil Wagner (2-50) claimed the remaining two wickets.
Pakistan resumed on 30-1 – in response to the Black Caps' imposing 431 first-innings total – and they were left reeling as New Zealand's four-man pace attack wreaked havoc early.
New Zealand quick Jamieson made the first breakthrough of the day – knocking over Abid Ali for 25 in the 13th over.
Trent Boult (2-71) joined in the action, dismissing Mohammad Abbas (five), while Azhar Ali (five) and Haris Sohail (three) followed shortly after as a pair of Tim Southee (2-69) wickets quickly left Pakistan five down and 62-5 at lunch.
Despite a fractured toe, Wagner claimed the wicket of Fawad Alam (nine), who was caught behind by BJ Watling, before Rizwan and Faheem thwarted the Black Caps.
Rizwan and Faheem made New Zealand toil hard in between three rain breaks but once Santner struck, the hosts quickly skittled Pakistan to take full control of the first of two Tests.
Mitchell Santner (2-52) took the decisive wicket with four overs to spare as the Black Caps were forced to be patient and take six wickets in the last session to seal a tense victory on the final day on Wednesday.
Pakistan batsman Fawad Alam and captain Mohammad Rizwan pieced together a gritty 165-run fifth-wicket partnership that swallowed up 62 overs from the opening two sessions.
Each of the five Black Caps bowlers claimed two wickets apiece as Neil Wagner (2-55) and Kyle Jamieson (2-35) took the key wickets of Rizwan and Fawad respectively.
Pakistan's tailenders were only 27 balls away from a memorable draw in the first of two Tests when Santner caught and bowled Naseem Shah (one), as the tourists lost 31-6 to finish 271 all out in their second innings.
Chasing 373 for victory, Pakistan resumed on 71-3 and the visitors appeared in some early trouble when Trent Boult (2-72) had Azhar Ali caught behind for 38 on the third ball of the day.
But the pair of Fawad and Rizwan dug in and rode their luck on occasions to reach 137-5 at lunch with Pakistan battling for the draw.
The duo made it to tea at 215-4 and, by the time the partnership was broken after more than 62 overs, Pakistan had reached 240-5 as Jamieson removed Rizwan lbw for 60 runs off 191 balls.
It was not enough to secure what would have been an unlikely win, though, with stumps on day five agonisingly called for bad light despite the hosts being just 15 runs short of their target, while New Zealand only needed one more wicket for victory.
Pakistan had been struggling on 80-5 as they chased a target of 319, but Sarfraz's terrific knock of 118 was ably supported by Saud Shakeel (32), who later added another partnership of 70 with Agha Salman (30) to almost take the win before the umpires called it with Pakistan on 304-9.
It was the fourth hundred of Sarfraz's Test career, justifying the decision to call him back into the team for this series, and he said after the draw: "Definitely I have more hundreds, but this was [my] fourth innings hundred and in the fourth innings. It is not easy to bat anywhere in the world, so I think this is my best hundred."
Sarfraz has an average of 38.85 from 51 Test appearances since his debut in 2010, and is just eight runs short of 3,000 as he ended the series with a total of 335 runs from four innings.
"I have been there with the team for four years and unfortunately I did not get a chance," he added. "But whatever cricket came my way, my effort was to keep playing my game and keep giving performances and if Allah wants then I would get an opportunity and I did get an opportunity.
"My state of mind wasn't very good when I came to bat the first time [in the series]. I was very tense, there was a lot of nerves. But the captain gave me a lot of confidence and the boys in the team gave me a lot of confidence. I backed my form from domestic cricket and had a good performance."
Michael Bracewell took 4-75, including the vital wickets of Sarfraz and Shakeel as New Zealand looked to close in on a win that would have secured them the series, which ended tied as both Tests culminated in draws.
Black Caps captain Tim Southee was in reflective mood, though, and praised Sarfraz for his defiance with the bat.
"We got ourselves to push for a win, but the way Sarfraz played sort of took the game away from us," he said. "It was a funny game, we saw in the end it was still up for grabs.
"We knew from the nature of the surface that things could happen late in the Test, Sarfraz was probably the difference, we could've won had we got them [out] earlier."
The 34-year-old Sarfraz replaces Azam Khan for the upcoming tournament two years after he was sacked as captain.
Haider takes Mohammad Hasnain's spot, while fellow batter Fakhar comes into the 15-man squad at the expense of Khushdil Shah.
The selectors opted to tinker with the initial squad they named after keeping a close eye on performances in the National T20 Cup.
Sohaib Maqsood has retained his place after there were doubts over his participation due to a back injury.
The batter underwent an MRI scan this week but has been cleared to travel for the tournament in the United Arab Emirates and Oman.
Pakistan start their quest for T20 glory with a mouthwatering Group 2 clash against fierce rivals India at the Dubai International Cricket Stadium on October 24.
Pakistan squad:
Babar Azam (captain) Shadab Khan, Asif Ali, Fakhar Zaman, Haider Ali, Haris Rauf, Hasan Ali, Imad Wasim, Mohammad Hafeez, Mohammad Nawaz, Mohammad Rizwan, Mohammad Wasim, Sarfraz Ahmed, Shaheen Afridi, Sohaib Maqsood.
West Indies pacer Jayden Seales praised his side’s bowling effort on day one of the first Test between the West Indies and Pakistan in Multan on Friday morning.
In a day shortened by foggy conditions at the Multan Cricket Stadium, the hosts, after winning the toss and choosing to take first strike, were restricted to 143-4 in 41.3 overs at stumps.
Jayden Seales delivered a stellar performance, as he snared three early wickets to give the West Indies a promising start in their opening Test against Pakistan at the Multan Cricket Stadium on Friday.
Pakistan appeared to be in the ascendancy early on Saturday when they quickly knocked off the final two wickets to limit West Indies' first-innings lead to 36, all out for 253.
But the tourists were 65-4 after Jayden Seales struck twice in the 26th over, suddenly struggling and just 29 in front.
Crucially, Babar and Mohammad Rizwan (30) then put on 56 for the fifth wicket, which belatedly arrived when play resumed following a break for the weather.
Captain Babar remained and he had 54* at stumps, still unbeaten with Pakistan on 160-5, 124 ahead.
Seales unsettles Pakistan
Teenage pace bowler Seales threatened to really upset Pakistan in a stunning over. After taking 3-70 in the first innings, the 19-year-old struck with the first ball of a new spell, drawing an edge from Abid Ali (34), and then added another as Fawad Alam was caught behind for a three-ball duck.
Rizwan and rain slow Windies
That Seales burst left Pakistan reeling, four down and scarcely leading. But Rizwan arrived for a vital turn with the bat, contributing to a partnership with Babar that reached 52 before an early tea was called due to the rain. He did not last much longer, but Rizwan allowed Babar to settle again.
After their opening game at Headingley was washed out, the teams endured another frustrating day in Cardiff as the umpires called off the third match without a single bowl being bowled.
England’s 23-run victory at Edgbaston on Saturday means they have an unassailable 1-0 lead in the series.
However, Pakistan have one last chance to level things at The Oval on Thursday before both teams head off to the United States for the T20I World Cup in June.