Opener Rohit Sharma made a composed 137 from 126 balls and Suresh Raina 65 from 57 as India recovered from 115-3 to post 302-6 at a boisterous MCG.

Bangladesh lost two wickets in the seventh over of their reply and eventually limped to 193 all out in 45 overs as India's bowlers dominated.

India meet either Australia or Pakistan in a Sydney semi-final on 26 March.

They will go there on the back of 11 successive World Cup victories, a run that stretches back to their success on home soil four years ago.

 Their six-match winning streak in this competition has come after a horrible tour of Australia, where they failed to win any of their 10 games across all formats.

But the resurgence in a limited-overs tournament is typical of MS Dhoni's team, who not only hold the World Cup, but also the Champions Trophy and won the 2007 World Twenty20.

India made the last four by outclassing a Bangladesh team that eliminated England on their way to a first World Cup quarter-final.

Initially, the Tigers were not overawed, despite being made to field first on a very good pitch as some accurate bowling and tight fielding stifled India in the first half of their innings.

However, the rebuilding done by Rohit and Raina in a stand of 122 ensured that India were able to accelerate as Bangladesh became ragged. The batting powerplay yielded 50 runs and the final 15 overs a total of 147.

They came together after Ajinkya Rahane miscued Taskin Ahmed to mid-off and a period when India failed to find the boundary for 11 overs.

Rohit, who drove the first ball of the match for four, had already seen Shikhar Dhawan stumped off Shakib Al Hasan and Virat Kohli caught behind from Rubel Hossain.

He and Raina steadied, then they timed their attack, though Bangladesh can have reason to feel aggrieved after Rohit survived being caught on the leg-side boundary when on 90 because a Rubel full-toss was wrongly deemed too high.

The right-hander completed a seventh one-day hundred and, despite Raina top-edging to the wicketkeeper, unfurled his full range of strokes.

Strong on the back foot throughout, Rohit was now sweetly timing through the covers and brutally pulling on the leg side.

Though he was yorked by Taskin, India still inched past 300 on a ground where no more than 297 has been reached to win a one-day international.

Bangladesh's bid to pull off both the highest Melbourne chase and win a first World Cup knockout match was derailed when two wickets fell in successive deliveries.

Tamim Iqbal edged Umesh Yadav to wicketkeeper Dhoni and Imrul Kayes was run out in a mix-up with new man Soumya Sarkar.

From there, Bangladesh never looked like threatening as the impressive India attack picked up regular wickets, the highlight being Dhawan's juggled catch on the fine-leg boundary to hold Mahmudullah off Mohammed Shami.

The enthusiastic crowd ensured a raucous atmosphere throughout, but the match drifted to an inevitable conclusion.