Suryakumar, 33, hammered 58 off 26 balls at Kandy's Pallekele in his first match as T20 skipper with India beginning a new era in the format after its T20 World Cup triumph last month.
India posted 213-7 and then bowled out the hosts for 170, after spinner Axar Patel struck twice in one over including taking the key wicket of Pathum Nissanka for 79.
Nissanka looked like setting up the chase, but Sri Lanka lost nine wickets for 30 runs to be bowled out in 19.2 overs.
"We practised here for two-three days and we knew how the wicket would play," said Suryakumar, who was named player of the match.
"We never thought it would go away from us, given we won the World Cup. Fortunately, there was no dew."
India have made a fresh start to T20 cricket after long-term stalwarts Rohit Sharma, Virat Kohli and Ravindra Jadeja announced their retirements from the format following their World Cup win in Barbados.
Suryakumar, who was picked as leader ahead of Hardik Pandya -- Rohit Sharma's deputy in the World Cup -- put on a key stand of 76 with wicketkeeper-batsman Rishabh Pant, who smashed 49.
Fast bowler Matheesha Pathirana took four wickets, including Suryakumar and Pant, but could not stop India from crossing 200 after a sloppy fielding effort by the home team.
Charith Asalanka was appointed new Sri Lanka T20 skipper following their early exit in the T20 World Cup and elected to field first after he won the toss.
Sri Lanka collapse
Both Sri Lanka and India have got new coaches as well, with Gautam Gambhir joining India and Sanath Jayasuriya named in an interim role for Sri Lanka.
Yashasvi Jaiswal, who smashed 40 off 21 balls, and Shubman Gill, who hammered 34, handed India an explosive start in a partnership of 74 in the first six overs.
The openers departed in the space of two deliveries with Dilshan Madushanka taking down Gill and leg-spinner Wanindu Hasaranga getting the left-handed Jaiswal stumped with his first ball.
Suryakumar steadied the innings and took on the opposition attack with eight fours and two sixes in a partnership with the left-handed Pant.
Pathirana, known as "Baby Malinga" for his slinging action and yorkers similar to former Sri Lanka quick Lasith Malinga, trapped Suryakumar lbw after the batsman's 22-ball fifty.
Pathirana then bowled Pandya and Pant.
In reply, Sri Lanka started strongly with an 84-run stand between Nissanka and Kusal Mendis, who made 45 off 27 deliveries.
Nissanka kept up the charge, despite losing Mendis in the ninth over, and smashed seven fours and four sixes in his 48-ball knock.
Patel, a left-arm spinner, bowled Nissanka and then sent back Kusal Perera in the same over, and soon Sri Lanka collapsed from 140-1 to 163-7.
"We could've done better (with the bat)," said Asalanka. "It (6-5 batting-bowling combination) is an experiment, but this is the way we should go in the future."
The second match of the series will take place on Sunday at the same venue.
