Mavi returned figures of 4-22 to help the hosts bowl out Sri Lanka for 160 in a victory target of 163 and lead the three-match series 1-0 in Mumbai. The 24-year-old Mavi was ably supported by fellow pace bowlers Umran Malik and Harshal Patel as they picked up two wickets each.
Axar Patel, a left-arm spinner, held his nerve in a tense last over when Sri Lanka needed 13 for a win and Chamika Karunaratne gave India a scare with his unbeaten 23. The final over witnessed a wide, to begin with, and ended with two run-outs to leave Karunaratne heartbroken and India jubilant.
Hardik Pandya, who captained India for the first time at home, praised Mavi, saying: "I have seen him bowling well in the IPL and I just told him to simply bowl. "I told him, 'I am backing you. Even if you get hit, it's fine."
Mavi said: "I was waiting for this moment for the last six years. Had injuries in between and it felt my dream will never come true."Deepak Hooda (41) and Axar (31) set up victory with an unbeaten 68-run sixth-wicket stand that steered India to 162-5 after being tested by the Sri Lankan bowlers.
'Really disappointing'
Ishan Kishan came out attacking as he hit Kasun Rajitha for a six and two fours in a 17-run opening over after the tourists invited India to bat. India raced to 26 in the first two overs but the momentum dipped after losing their top and middle-order before Hooda, who hit four sixes in his 23-ball knock and was named man of the match, and the left-handed Axar took charge.
Debutant Shubman Gill began with a boundary but soon fell lbw for seven to mystery spinner Maheesh Theekshana. Sri Lanka hit back with disciplined bowling and Karunaratne sent back Suryakumar Yadav after the batsman mistimed one of his audacious scoop shots to be caught at short fine leg.
India lost two more wickets and slipped to 77-4 when wrist spinner Wanindu Hasaranga got the left-handed Kishan out for 37. Left-arm quick Dilshan Madushanka added more misery to the opposition's batting as he got Pandya caught behind for 29.
In reply, Mavi struck in his first over of international cricket as he bowled Pathum Nissanka for one. He then sent back Dhananjaya de Silva for eight in his next to put India on top. Sri Lanka kept losing wickets with tearaway quick Umran getting Charith Asalanka out for 12 and Harshal struck twice to leave Sri Lanka on 68-5. Harshal cut short Kusal Mendis' knock on 28 with his medium-pace bowling and then sent back the dangerous Bhanuka Rajapaksa for 10.
Skipper Dasun Shanaka and Hasaranga attempted to put the chase back on track in a 40-run partnership but Mavi broke the stand with the wicket of Hasaranga for 21. Shanaka, who made 45, kept up the attack as he hit Umran for a six in the 17th over but the speedster had his revenge two balls later to further dim Sri Lanka's hopes.
"Really disappointing with the way we finished," said Shanaka. "It is still the first game and they (batters) are a really good bunch of youngsters, they will come good."
The second match is on Thursday in Pune.
Brief scores: India: 162/5 in 20 overs (Ishan Kishan 37, Deepak Hooda 41 not out, Axar Patel 31 not out) Sri Lanka: 160 all out in 20 overs (Kusal Mendis 28, Dasun Shanaka 45; Shivam Mavi 4/22)
