England 219 (Pope 62, Yasir 4-66) and 277 for 7 (Woakes 84*, Buttler 75, Yasir 4-99) beat Pakistan 326 (Masood 156, Azam 69, Broad 3-54) and 169 (Yasir 33, Broad 3-37) by three wickets
Buttler's gutsy knock of 75 from 101 balls in the face of mounting criticism over his place in the side, combined with Woakes' new-found form with the bat, handed England an unlikely victory and broke their run of five consecutive series in which they had lost the first match.
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Under pressure to make runs after his Test average had dipped and a torrid time behind the stumps during this match, Buttler came in with England 106 for 4 chasing a target of 277 for victory.
He and Woakes, who had a high score of 37 not out from his previous 17 innings, shared a partnership worth 139 for the sixth wicket and helped England pull off the second-highest fourth-innings run chase at Old Trafford.
Fittingly, Woakes hit the winnings runs with a four through third man off Shaheen Shah Afridi to finish not out on 84 as England snatched victory by three wickets inside four days.
Joe Root began the day suggesting a target below 260 would be within reach. Pakistan pushed it just beyond after Yasir Shah came out, as expected, and threw the bat.
Yasir resumed on 12 with Pakistan 137 for 8 and leading by 244. He clubbed 21 from nine balls, including 11 off Jofra Archer's first four deliveries of the day, followed by a defiant four past mid-on and a brutal six over midwicket off Stuart Broad's first three.
Broad had the final say two balls later, drawing a wild swing from Yasir to a length ball outside off and finding a thick edge which went through to Buttler behind the stumps. But Yasir's job was done.
In all, Pakistan pilfered 32 runs within the first half hour, before Naseem Shah was the last man out, bowled by Archer for 4.
England managed just 22 runs from the first 11 overs of their chase but, with the best part of two days ahead of them, time was the least of their worries.
Wickets were, and Mohammad Abbas took the first with the first ball of the 12th, which nipped back and struck Rory Burns on the back leg as it curled in off the seam. Burns was quick to call for a review, but his dismissal was confirmed on umpire's call with the ball hitting the top of middle stump.
There appeared to be words exchanged, with Burns turning to the Pakistan team and putting a finger to his lips as he strode from the field.
Dom Sibley and Root pressed on to 55 for 1 by lunch but there was a period after the break where England's scoring went quiet against Abbas and Yasir and they managed just two runs in 29 balls.
Yasir, who had claimed four England wickets in their first innings, broke a 64-run partnership when he had Sibley caught by Asad Shafiq for 36, the opener furious with himself after attempting a drive and sending a thick edge straight to slip.
His dismissal brought Ben Stokes - and all his promise - to the crease and England's own "miracle worker" got off the mark with a boundary through third man off Naseem. Crucially, though, Naseem swooped quickly to remove the other set batsman, when he found Root's outside edge, which was collected by Babar Azam at slip to send him out on 42.
With England 96 for 3 and needing 181 runs more to win, the glare on Stokes intensified, even though they also had Ollie Pope, who had top-scored for the hosts in their first innings, at the crease.
If any indication was needed as to just how highly prized Stokes' wicket is, Pakistan burned an ambitious review when Naseem struck him on the pad with a ball that looked to be going down the leg side. Sure enough Hawk-Eye showed it was missing and Stokes survived.
To Pakistan captain Azhar Ali's credit, however, faced with the prospect of using up another review seven balls later, when Yasir believed he had Stokes caught behind with a googly that bounced out of the rough outside off stump, Azhar went for it. His courage was rewarded when UltraEdge showed the ball had brushed the glove on the way through to Mohammad Rizwan, who gathered the ball high at his second grab.
England had lost 3 for 20 and their situation worsened three overs later. Pope could do little about his dismissal when he copped an unplayable delivery from Afridi that reared off a length and hit his top hand, ballooning to Shadab Khan running in from gully.
With England 117 for 5 and hope fading fast, still 160 runs from victory, Buttler and Woakes played a stunning hand that rescued their side.
With Buttler's white-ball credentials in no question, he combined the skill to rack up the runs at a good tempo with the patience required to not throw his wicket away. Even when he did fall, attempting a reverse sweep off Yasir and struck on the boot for an lbw decison he challenged and lost, Woakes was well set and the hard work was done.
Needing 21 more runs, England promoted Broad, and although he fell cheaply, lbw to Yasir with the second new ball, Woakes saw them home to end a miserable run in first Tests (aside from a one-off win over Ireland) that stretched back to the start of 2019.