Last night, Yadav, making good use of pace and bounce, finished with four for 31 from his nine overs. Shami's two for 37 pushed him to 17 wickets, top of the cup wicket taking list, and at a cost of only 13.29 apiece.
Sharma has taken 11 at 21.72, while Yadav's 14 have cost 17.78.
Add in the classy offspin of Ravi Ashwin - 12 wickets at 24 - and it's no wonder India have bowled all seven opponents out in the cup.
''The bowling was something we definitely wanted to improve. It was a bit of a concern for us," captain MS Dhoni said last night.
''In this tournament the bowlers have done their job well. You have to keep putting the intensity into the net sessions and everything is shaping up."
Bangladesh did have India in a jam during their innings, at one point not conceding a single boundary in 65 balls.
However man of the match Rohit Sharma and pugnacious lefthander Suresh Raina regained the initiative with a 122-run fourth wicket stand, with Raina hitting a breezy 65 in 57 balls which got the momentum back into India's innings. They put on 176 in the last 20 overs, 57 from the last five.
No team has successfully chased over 300 to win an ODI so the odds were heavily against Bangladesh. Several batsmen got starts but none could press on, as they were bowled out for 193.
However, their first trip to the quarter-finals shows Bangladesh have much to look forward to, with several young players making their mark at the cup.
''Most of our players are really starting on their careers and the boys should be very happy with their efforts," captain Mashrafe Mortaza said. ''Hopefully we'll carry on from here."
Certainly the combined talents of the likes of Mahmudullah, Soumya Sarkar, Tamim Iqbal, Mushfiqur Rahim, Shakib al Hasan, Rubel Hossain and Taskin Ahmed hint at the makings of a good team.
But it's India who march into the last four. They were not widely tipped to shine in the Australasian-based tournament, especially on the back of their poor tour of Australia, and getting well beaten in New Zealand last summer.
Those thoughts have been banished on the back of a series of assertive displays. Two wins will enable them to join the West Indies and Australia in having won the cup back to back.
New Zealand play the West Indies in the fourth quarter-final in Wellington on Saturday.