Mendis (57) and Perera (74) toyed with the Bangladesh attack with a flurry of boundaries and sixes, to the delight of the home crowd at the Premadasa Stadium.
Invited to bat after a drizzle delayed the toss by 15 minutes, Sri lanka were off to a flying start with Mendis putting on 56 runs for the opening wicket with Danushka Gunathilaka (26).
Bangladesh pacers were guilty of bowling short and the Lankans took full advantage of that, pummelling them for 70 runs in the six mandatory powerplay overs.
That the visitors persisted with bowling short despite getting smacked, too helped Sri Lanka's cause.
Mendis hit 57 off 30 balls with the help of five sixes and two fours, Perera found the fence eight times and cleared it twice in his 48-ball knock.
That set the tone for a big total and even though Mustafizur Rahman cleaned up Gunathilaka, the hosts were sitting pretty at the halfway stage at 98 for one.
There was a lull though, from seventh to ninth over, as the hosts managed just 16 runs in 18 balls.
The well-settled Mendis hoiked Nazmul Islam over square leg for a six to break the shackles.
Continuing his stellar run at the top, Mendis meanwhile welcomed Mustafizur with a six and brought up his fifty in just 26 balls, his third half-century in four innings.
Bangladesh had a breakthrough but not before Mendis sent a Mahmudullah delivery soaring over deep mid-wicket for another maximum.
Dasun Shanaka and Dinesh Chandimal fell cheaply but Upul Tharanga helped Sri Lanka score 17 runs in the 17th over with the help of two boundaries and a six. Tharanga was unbeaten on a breezy 32 off 15 balls.
Meanwhile, Perera continued his onslaught on the Bangladesh bowlers, and was mostly dealing in boundaries. He got out while going for one too many, getting stumped off Mustafizur.
Mustafizur Rahman (3/48) and Mahmudullah (2/15) were the most successful bowlers for Bangladesh.
Sri Lanka entered the game high on confidence, having comfortably beaten India in the tournament opener and their recent record against Bangladesh gave them the edge.
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