Riding on half-centuries from Lokesh Rahul (54) and Shikhar Dhawan (52), India scored 201-6 after being made to bat first.
Sri Lanka was all out for 123 runs in 15.5 overs with only two batsmen getting double figures.
India won the second T20 in Indore by seven wickets while the first T20 in Guwahati was washed out.
Rahul and Dhawan gave India a fiery launch with sharing 97 runs off 65 balls for the opening wicket.
Rahul reached his latest half-century from 34 balls. He hit five fours and a six.
Dhawan also overcame a slow start to get a confidence boosting half-century off 34 balls.
The Sri Lanka spinners led a comeback by the visitors. India was pegged back from 97-0 to 122-4 in the space of two overs.
India replaced Rishabh Pant with Sanju Samson, who batted No. 3 but lasted two balls before he was out lbw for 6.
Rahul and Dhawan fell on either side of his dismissal.
Shreyas Iyer's wicket for 4 put India in a bit of hole as spinner Lakshan Sandakan took 3-35 in four overs.
Virat Kohli (26 off 17 balls) and Manish Pandey added 42 runs for the fifth wicket to put India back in charge. Kohli was run out in the death overs while Pandey smacked 31 not out off 18 balls, including four fours.
Shardul Thakur smashed 22 not out off eight balls, with one four and two sixes, as India passed 200 and set a challenging total.
"We did well in both games, chasing in one and setting a target in the other," Kohli said,
"We were very clinical. The middle order collapse was challenging but we recovered well to post 200."
Sri Lanka's chase got off to the worst start possible, and it was soon reduced to 26-4 in the sixth over.
Opening bowlers Jasprit Bumrah (1-5) and Thakur (2-19) were productive but Navdeep Saini did the most damage once again with his pace and returned 3-28 in 3.5 overs.
Saini was named man of the series for his showings in Indore and Pune.
"When I used to play with the red ball, I found white ball cricket tougher," Saini said. "Now, after practicing and playing more matches, it is getting easier. The senior bowlers help me a lot. Bowling fast comes naturally to me."
The India spinners took some stick as a fit-again Angelo Mathews scored 31 off 20 balls, and Dhananjaya de Silva hit 57 off 36 balls. They shared 68 runs for the fifth wicket, but they were managing to only delay the inevitable.
The last six wickets fell for 29 runs in 23 balls. Offspinner Washington Sundar took 2-37.
India's next assignment is three one-day internationals against Australia from Tuesday in Mumbai.