Chasing 175 for a win in the first match of the tournament, which also features Bangladesh, Sri Lanka lost their way in the middle overs but ultimately reached their target with nine balls to spare.
Put in to bat first, India got off to a wobbly start but recovered through a fine 90 from opening batsman Shikhar Dhawan to post a challenging 174 for five in their 20 overs.
Sri Lanka lost Kusal Mendis for 11 in the second over of their chase but Perera and Danushka Gunathilaka put the Indian bowlers to the sword during a 58-run second-wicket stand in just 3.3 overs.
India seamer Shardul Thakur conceded 27 runs in the third over of the innings with Perera smashing five fours and a six in that over to wrest momentum for his side.
The left-hander completed his half-century in 22 balls and hit six fours and four sixes in his knock before being out stumped to off-spinner Washington Sundar.
Sri Lanka also lost Upul Tharanga to leg-spinner Yuzvendra Chahal cheaply to suffer a minor hiccup before all-rounder Thisara Perera hit 22 off 10 balls to take the side home.
Earlier, India's batting got off to a false start with the fall of stand-in captain Rohit Sharma and Suresh Raina in the first two overs.
Leading the side in the absence of the rested regular captain Virat Kohli, Rohit fell without scoring and it was left to Dhawan and Manish Pandey to lift the side through a third-wicket stand of 95.
Gunathilaka dismissed the dangerous Dhawan, who hit six fours and an identical number of sixes in his 49-ball knock, while Pandey made 37.
The second match of the tournament will be played between Bangladesh and India at the same venue on Thursday.
(Reporting by Sudipto Ganguly in Mumbai; editing by Christian Radnedge)
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