Big-hitting opener Sharma smashed 83 off 55 balls to help India overcome a shaky start to score 166-6 before some excellent bowling by left-arm pacer Ashish Nehra and other medium pacers restricted hosts Bangladesh to 121-7.
One-down Sabbir Rahman made the highest 44 off 32 balls for Bangladesh after an early innings jolt saw the home side lose both their openers Mohammad Mithun (one) and Soumya Sarkar (11) for 15 runs.
Bangladesh could never recover from the damage and kept losing wickets at regular intervals as experienced Nehra finished with 3-23.
Indians Jasprit Bumrah, Hardik Pandya and Ravichandran Ashwin claimed one wicket each, and all conceded 23 runs.
Bangladesh earlier opted to bowl first on a rain-soaked pitch and made good use of the conditions to put India in trouble early in their innings at the packed Sher-e-Bangla National Stadium.
Al Amin Hossain bowled opener Shikhar Dhawan for two before skipper Mashrafe Mortaza got rid of an in-form Virat Kohli, who offered an easy catch to Mahmudullah at mid off for eight, putting India’s formidable batting on the back foot.
Indian cricketer Ashish Nehra reacts after the dismissal of Bangladesh batsman Mohammad Mithun in Dhaka on February 24, 2016 © AFP Munir uz ZamanWith the first six overs yielding just 31 runs, India began to feel the pressure once Mahmudullah bowled Suresh Raina for 13 to leave the visitors struggling at 42-3.
Sharma and Yuvraj Singh steadied the innings with a 55-run fourth wicket partnership before Pandya, who scored 31 off 18 balls, joined the opener to provide India a much-needed impetus.
Sharma was dropped by Shakib Al Hasan on 21 off Taskin Ahmed and he promptly made Bangladesh pay dearly as he hit two fours and a six in the next three balls of the over.
He struck seven fours and three sixes for his 10th half-century in a Twenty20 international.
“It’s important for me to start afresh and not look back too much,” said man of the match Sharma.
“This is a perfect platform for us before the World Cup (World Twenty20),” he said.
“I was focusing on my basics on this kind of the pitch, use the pace of the bowlers. It was a good wicket and the ball was carrying.”
Skipper MS Dhoni, who passed a late fitness test to play the game, reserved some praise for young all-rounder Pandya.
“Batting fearlessly is Hardik (Pandya)’s strength and that’s why we want to give him more matches, he’s a good fielder too and a useful third seamer,” said Dhoni.
Sri Lanka will face the United Arab Emirates in the second match of the tournament at the same venue on Thursday.