Morgan came in on a hat-trick after leg-spinner Shadab Khan had reduced England, who were chasing a stiff victory target of 196, to 66/2.
But the Irishman made a blistering 66 off just 33 balls and with fellow left-hander Dawid Malan (54 not out) took the game away from Pakistan during a third-wicket stand of 112.
Victory, achieved with five balls to spare on a sunny afternoon, saw the 50-over world champions go 1-0 up in a three-match series following Friday’s rain-marred no result in Manchester.
The 33-year-old Morgan considered his international future after leading England to World Cup glory with a dramatic Super Over win in last year’s final at Lord’s. But it now looks as if he will lead England at the 2021 T20 World Cup in India.
Asked if he was playing better than ever, Morgan told Sky Sports: “I think I am and that is backed up by stats over the last couple of years, they’ve been the most productive of my whole career which is great.
“If I can combine a little of that form with experience, then hopefully it will contribute to more wins,” the player of the match added.
This was the highest successful chase against Pakistan in a Twenty20 international, surpassing Australia’s 199/7 in a thrilling 2010 World Twenty20 semi-final in St Lucia.
Veteran batsman Mohammad Hafeez made 69 in Pakistan’s 195/4 that also featured 56 from captain Babar Azam, the world’s number one-ranked Twenty20 batsman.
“Our total was good but we didn’t bowl well, we struggled with our bowling,” said Babar. “Credit goes to Malan and Morgan for how well they played.
“We’ll learn a lot from this series. Under pressure, I need to handle the bowlers and tell them a few things,” added the 25-year-old novice skipper.
Pakistan’s cause was not helped when they had to reshuffle their attack after left-arm quick Mohammad Amir limped off having bowled just two overs.
“He’s feeling pain in his right hamstring, it’s been iced and they (Pakistan’s medical staff) will see him tomorrow (Monday),” a team spokesman told AFP when asked if Amir would be fit for Tuesday’s series finale, also at Old Trafford.
Jonny Bairstow and Tom Banton got England’s chase off to a sound start. But a partnership of 66 ended when Bairstow, on 44, miscued Shadab to short fine leg.
Next ball, with the batsmen having crossed, Banton – fresh from 71 on Friday, his first T20 international fifty, was lbw for 20.
Morgan survived the hat-trick delivery but could have been lbw for a second-ball duck to Shadab, only for a tight umpire’s call verdict to fall in the batsman’s favour. Shadab finished with fine figures of 3/34.
Morgan’s fourth six, off left-arm fast bowler Shaheen Afridi, saw him to a 27-ball fifty before he holed out in sight of victory.
Malan might have missed this match had not England been fielding separate red and white-ball squads in a coronavirus-affected season, with batsmen such as Test captain Joe Root and Jos Buttler omitted from this series.
But his 35-ball half-century was his seventh score of fifty or more in just 12 Twenty20 internationals and Malan finished the match when he cut Afridi for four.
Earlier, Babar and Hafeez were severe on an England attack where leg-spinner Adil Rashid was the stand-out performer with 2/32.