In reply, England stuttered to 49-3 in the sixth over as they struggled to get any momentum against a fiery pace attack, with boundaries hard to come by.
But Stokes and Moeen Ali (19) used their experience and cool heads to guide England to 138-5 with six balls to spare, climaxing a riveting tournament that spanned 45 games over nearly a month.
"He always stands up in the biggest moments, he's a man who can take a lot of pressure on his shoulders and perform," Buttler said of Stokes.
"When he's there you know you have a good chance. He's a true match-winner. He's one of the great players of English cricket."
Curran added that "we all look up to him. People question him, but he's incredible".
Stokes insisted the bowlers deserved the credit
"In finals, especially when chasing, you probably forget all the hard work before that. To restrict them to 130, the bowlers have to take a lot of credit. Adil Rashid and Sam Curran won us the game," he said.
The victory added to the 50-over title England won in 2019, building on the legacy of former captain Eoin Morgan, who retired this year after transforming the team into a white-ball juggernaut.
It was England's second T20 crown after tasting success in 2010, joining the West Indies as the only two-time winners since the tournament's inception in 2007.
The game was billed as a showdown between Pakistan's attack and England's top order, and Shaheen Afridi bowled danger man Alex Hales in the first over of the run chase.
But that only fired up Buttler who smashed two boundaries off Naseem Shah. Phil Salt, playing in place of the injured Dawid Malan, made 10 before pulling Haris Rauf to Iftikhar Ahmed
The ball was swinging and seaming and the menacing Rauf claimed the key wicket of Buttler, edging to wicketkeeper Mohammad Rizwan after the skipper had scored 26 off 17 balls.
'20 runs short'
The runs dried up as England reached 77-3 at halfway, compared to Pakistan's 68-2 after 10 overs.
Harry Brook came undone on 20 against the spin of Shadab Khan, holing out to Afridi who injured himself taking the catch and it came down to needing 41 runs off five overs.
Stokes relieved the pressure with a four and a six off Ahmed before hitting the winning run.
"Congratulations to England, they deserve to be champions and fought well," said Pakistan captain Babar Azam.
"I just told the boys to play our natural game, but we fell 20 runs short and the boys fought well with the ball. Our bowling is one of the best attacks in the world."
With forecast rain staying away, England produced disciplined and economical bowling to stymie 2009 champions Pakistan, with Shan Masood's 38 the top score.
Openers Rizwan and Azam shared a century partnership in their semi-final against New Zealand, but this time Rizwan dragged a delivery from Curran on to his stumps on 15.
The introduction of Rashid soon after the six-over powerplay reaped an immediate reward with Mohammad Haris (8) attacking him on his first ball only to sky a simple catch to Stokes.
Masood began swinging the bat in the second half of the innings, hitting a four and six off Liam Livingstone.
But once again Rashid got the breakthrough, pulling off a diving catch from his own bowling to claim the vital wicket of Azam, whose 32 came off 28 balls.
Ahmed only lasted six balls before Masood and Shadab Khan (20) fell in the space of two runs as Curran and Chris Jordan kept the lid on any hope Pakistan had of a late flurry.