Dhaka: Harbhajan beat Junaid Siddique and MSD did the rest behind the stumps to hand India a most wanted breakthrough as India put the brakes on Bangla scoring.
Bangladesh had a dream start after Indian bowlers failed to control the scoring.
Few more overs from Harbhajan Singh and others could create serious runrate issues for the Bangala side.
Earlier, Virender Sehwag smashed a career-best 175 off 140 balls to power India to 370-4 after they were asked to bat by Bangladesh in the opening match of the World Cup on Saturday.
A sell-out crowd of 25,000 at the Sher-e-Bangla stadium watched in stunned silence as the aggressive opener lashed 14 boundaries and five sixes in his 14th one-day century.
Young Virat Kohli chipped in with 100 not out to leave the Tigers with a daunting target of 7.5 runs an over in the first Cup game between the two sides since Bangladesh upset India in the previous edition in 2007.
Sehwag narrowly missed his pre-tournament aim to bat out the full 50 overs, just as his team-mate Sachin Tendulkar had done last year while scoring the first-ever 200 in one-day cricket.
He was bowled by Bangladesh captain Shakib Al Hasan in the 48th over soon after equalling former Indian skipper Kapil Dev's score of 175 against Zimbabwe during the World Cup winning campaign in 1983.
Sehwag hit the first ball of the tournament for a four, rocking on the backfoot to punch Shafiul Islam to the cover fence, before reaching his half-century with a six.
Sehwag and Tendulkar hammered 69 for the first wicket by the 11th over when Bangladesh broke through with a stroke of luck.
Tendulkar drove a ball to mid-on and charged down the wicket, but found no response from the other end to leave both batsmen at the non-striker's end.
Shakib's direct throw to the wicket-keeper ended the world batting record holder's innings of 28.
Gautam Gambhir continued the run spree by adding 83 for the second wicket with Sehwag before he was bowled off Mohammad Mahmudullah's second delivery for 39.
Sehwag had scored half the team runs when he reached his first one-day century against Bangladesh in the 32nd over, adjusting his strokeplay on a wicket where the ball came slowly off the wicket.
Kohli took over after Sehwag suffered a leg injury and called for a runner in the 38th over, stroking eight boundaries and two sixes during a third-wicket stand of 203 with his Delhi captain.