Legspinner Yuzvendra Chahal finished with a staggering six wickets for 25 runs as England, chasing 203 to win, collapsed from 119-2 to 127 all out.
On a brilliant batting surface, Suresh Raina (63 off 45 balls) and MS Dhoni (56 off 36) earlier struck blistering fifties for India, the latter's first in his 76 T20Is.
England were well placed after 12 overs of their reply, but then Eoin Morgan (40 off 21) and Joe Root (42 off 37) fell to consecutive Chahal deliveries to trigger the dramatic collapse - eight wickets falling for eight runs in 19 deliveries.
For the third consecutive match, Morgan won the toss and elected to field first, and his side got off to an ideal start when India skipper Virat Kohli (2) was run out in the second over.
Raina countered, striking five sixes in his innings, while KL Rahul (22 off 18) hit two of his own, one an absolutely monstrous strike down the ground off Moeen Ali that cleared the roof.
Rahul was out an over later though, bowled when missing with an ugly hack across the line at a straight ball from Ben Stokes (1-32), though replays showed the bowler had got away with a no-ball.
Dhoni - promoted up the order after criticism for batting too low in the second T20I - continued the big-hitting onslaught, as he and Raina notched half centuries, though the latter was put down by Adil Rashid off his own bowling when on 47.
Raina did finally depart in the 14th over when miscuing the returning Liam Plunkett - in for Liam Dawson - to Morgan at extra cover.
Yuvraj Singh (27 off 10) took a bit of time to settle before then launching a blistering attack on Chris Jordan (1-56) in the 18th over, firing him away for three straight sixes.
Expecting pace on the ball again as Tymal Mills (1-32) bowled the next, Yuvraj was utterly bamboozled by a brilliant slower ball that he edged behind to Jos Buttler.
Though Dhoni and Hardik Pandya - run out - fell in Jordan's final over, India still managed to lift their score beyond 200, leaving England a testing chase.
The visitors will have been briefly worried when Ashish Nehra appealed loudly for lbw against Jason Roy to the very first ball, but the opener survived the scare.
His partner Sam Billings was not quite so fortunate as he fell to his first delivery, edging Chahal onto his pad and to Raina at slip.
It was part of an eventful first over from the legspinner as Roy sensationally reverse-swept six, and then Chahal missed the opportunity to run him out by throwing to the wrong end when Roy was stranded.
Roy (32 off 23) and Root kept England up with the rate, the visitors 55-1 at the end of the six-over powerplay, before Roy then fell in Amit Mishra's first, top-edging an attempted sweep off the legspinner.
Mishra (1-23) was proving a particular thorn in England's side, bowling two boundary-less overs to end his spell either side of a one-over Raina experiment that cost 22 as Morgan tonked the offspinner for three sixes.
With the run-rate climbing, Morgan and Root - who was dropped in Mishra's previous over - fell to consecutive Chahal deliveries and England fell apart thereafter.
Buttler departed for a duck in Jasprit Bumrah's next over, top-edging an attempted pull, before Chahal dismissed Moeen (2), Stokes (6) and Jordan (0) in his final over, to claim his six-for.
Bumrah (3-14) then swiftly wrapped up the innings, the match, and the series, as Plunkett and Mills were blasted out without scoring.