After Jeremy Bray's stumps were splattered, solitary slip Yusuf Pathan collected two excellent catches.
Sachin Tendulkar (39), Virender Sehwag and Irfan Pathan (both 35) were responsible for India's flying start.
They played so well, and at the end of the innings Yusuf (Pathan) got 50.
Pathan, who had celebrated his 21st birthday on Thursday, was eventually relieved after eight overs.
Pathan tries to shovel the ball over short fine leg but they can only manage one.
Pathan, playing for the first time in the series, was India's most expensive bowler.
India's left-arm paceman Irfan Pathan was named Man of the Match for his match haul of 9-111.
Pathan began the slide by dismissing Habibul Bashar and Rajin Saleh with successive deleiveries and took 3-32.
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Only Pathan joined them in double figures as India lost their last seven wickets for 63 runs.
Solanki was trapped plumb in front by Irfan Pathan one ball after hitting his second one-day fifty.
Earlier, Dravid, Mahendra Dhoni and Irfan Pathan were all out caught at point or gully after loose cuts.
Meanwhile, Munaf Patel replaces left-arm seamer RP Singh, who was deemed surplus to requirements along with all-rounder Yusuf Pathan.
Bell showed some signs of a return to form with six boundaries, including a sweet cover drive off Pathan.
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Pathan, earlier unimpressive with the new ball, returned in the 44th over for a spell he will want to forget.
But now, the promotion of Pathan, Dhoni and Yadav in the batting order has been part of a planned strategy.
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But Bangladesh soon found themselves in trouble as Pathan bowled Bashar through the gate for two and then had Saleh lbw.
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So confident were India of beating their demoralised opponents, that they opted to rest Sachin Tendulkar, Irfan Pathan and Harbhajan Singh.
Bouyed by that early success, Pathan then had Mahela Jayawardene picked up at square leg, before removing Sangakkara and Tillakartne Dilshan.
Solanki and Darren Maddy made decent enough progress, picking up sixes each before the latter was pouched at mid-on off Irfan Pathan.
Pietersen crashed Pathan over long-on for two sixes and was ably supported by Patel, who lifted Sehwag for two maximums of his own.
Irfan Pathan struck a huge six off spinner Brad Hogg in his 63-ball 26, while Tendulkar played some majestic drives to collect nine fours.
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He earlier returned figures of 3-35 during the Bangladesh innings as he and Irfan Pathan dashed the Tigers' hopes of posting a big total.
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Kumble's 10-wicket performance moved him five places up the ICC Test player rankings to fifth, while Irfan Pathan moved up a spot to 10th.
Pathan, who found plenty of swing movement throughout, removed Sanath Jayasuriya in the first over and also dismissed three others in the top six.
India made five changes with Ganguly, pace bowlers Irfan Pathan and Zaheer Khan, wicket-keeper Mahendra Dhoni and off-spinner Harbhajan Singh included in the team.
Sri Lanka made a positive start to their herculean task, but lost Avishka Gunawardene, who was lbw to Irfan Pathan after striking two early fours.
It is, however, true of Indian fast bowler Irfan Pathan, whose love of the game resulted in a scolding for him and younger brother Yousuf.
But Virender Sehwag has been dropped after a poor run of form in South Africa, while Anil Kumble and Irfan Pathan have also been axed.
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The third ball is a yorker, Dhoni can only dig it out for a single. 15 needed from three - Pathan needs to hit sixes.
Pathan finished with an 18-wicket haul in the tournament, justifying his billing as the best young pace bowler in the sub-continent, as India clinched the title.
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