Set a challenging 273 to win in Dhaka on Sunday, a rain delay that halted play for almost three hours saw India’s target reduced to 150 runs in 26 overs via the Duckworth-Lewis method.
And the efforts of Rahane and Robin Uthappa (50) ensured a below-strength India won with seven balls to spare in the series opener.
The likes of MS Dhoni, Virat Kohli and Ravichandran Ashwin have been rested for the three-match series, with Suresh Raina leading the makeshift side.
Bangladesh recovered from a slow start that saw both Tamim Iqbal (zero) and Mominul Haque (six) fall to paceman Umesh Yadav (3-48 off nine overs).
Anamul Haque was dropped by Raina on 19 and finished with seven fours in his 44 while captain Mushfiqur Rahim and Shakib Al Hasan added 59 and 52 respectively.
Anamul picked out Ambati Rayudu at deep mid-wicket to give debutant Parvez Rasool (2-60 off 10) his first wicket though, and he added another when Mushfiqur was caught at mid-off in the 31st over.
Skipper Raina (1-24 off five) then claimed the prize scalp of Shakib in the 42nd over when he was caught and bowled.
Mahmudullah hit 41 from 44 deliveries and Nasir Hossain chipped in with 22 but India bowled well in the latter stages, finishing with five wickets in the last nine overs.
Also making his one-day international bow, Akshar Patel finished with 1-59 off 10 overs while leg-spinner Amit Mishra took 2-55.
India’s chase started superbly as Rahane and Uthappa added 99 for the first wicket inside 17 overs.
Uthappa – who hit three fours and three sixes in his 44-ball knock – departed just before the heavens opened, controversially adjudged lbw off the bowling of Shakib (2-27 off six).
India’s fast start meant they were in an excellent position when play finally resumed and although Cheteshwar Pujara fell for a fifth-ball duck, also to Shakib, Rahane steered them towards victory.
The opener, who was perhaps lucky to avoid being given out lbw on two in the second over, eventually fell to Mashrafe Mortaza (1-25 off five).
But Rayudu (16 not out) and Raina (15 not out) were on hand to guide India to victory with more than an over remaining.
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