India reached 201-3 with eight balls to spare in reply to England’s 198-9 at the County Ground.
Virat Kohli scored 43 before he was caught and bowled by Chris Jordan, and Hardik Pandya (33 not out) shared a 50-run unbeaten partnership with Sharma.
Pandya hit the winning runs with a six over the long-on boundary.
England was sent into bat after India won the toss and got away to a positive start.
Jason Roy blasted 67 runs off 31 deliveries, including seven sixes, and Jos Buttler hit 34 off 21. The opening pair put on 94 before Buttler was bowled by Siddarth Kaul (2-35) at the end of the eighth over.
Roy was caught behind shortly after off the bowling of Deepak Chahar.
Pandya was India’s most successful bowler with a return of 4-38 from four overs.
In reply, Sharma moved to exactly 100 off 56 deliveries – with 11 fours and five sixes – and joined New Zealander Colin Munro as the only two players with three international tons in the sprint format.
Sharma — man of the match and series — said conditions and size of the pitch were ideal for his assault on the England attack.
“We always knew it was going to be a good pitch,” Sharma said. “The idea was to hold the ship and try and play big shots and that’s exactly what I did. I tried to spend some time in the middle, took my time and then went on to play those shots.”
India won the first T20 by eight wickets at Manchester before England leveled the series with a five-wicket win at Cardiff.
Ben Stokes returned for the decider as England dropped Joe Root to make room for the fit-again all-rounder.
The tourists made two changes, bringing seamer Chahar in for an international debut in place of Bhuvneshawar Kumar, who has a stiff back, while Kaul was in as an extra pace bowler, with Kuldeep Yadav surprisingly making way.
“It was tremendous with the bat,” England captain Eoin Morgan told Sky Sports. “Jason Roy and Jos Buttler proved what a dominant force they are up top and created a great platform for us to capitalize on and we didn’t do it justice … when a guy like Rohit goes out and peels off a hundred it’s very difficult to defend on a ground like this.”