Put into bat at the Wankhede Stadium in Mumbai, India struggled to impose themselves until a 68-run partnership between Deepak Hooda (41) and Axar Patel (31) for the sixth wicket gave the hosts a much-needed boost and pushed them to a total of 162.
Sri Lanka's chase then got off to a catastrophic start as Mavi struck early with the ball to remove Pathum Nissanka and Dhananjaya de Silva.
Mavi later added the scalps of Wanindu Hasaranga and Maheesh Theekshana to cap a dream debut.
Sri Lanka captain Dasun Shanaka provided some resistance, scoring 45 off 27, but his side were unable to build on his knock and fell just short of their target.
"I was waiting for this moment for the last six years. Had injuries in between and it felt my dream will never come true," Mavi said.
The second T20I of the series will be held at the Maharashtra Cricket Association Stadium in Pune on Thursday.
