Raina followed his maiden hundred against Hong Kong and 84 against Pakistan with an unbeaten 116 to help India overhaul Bangladesh's 283-6 with 6.4 overs to spare at the National Stadium.
For Bangladesh, Alok Kapali hit a maiden century but his brilliant work was spoiled by shoddy fielding, with three vital catches going down.
The 21-year-old Raina, dropped by Mashrafe Mortaza off Mahmudullah Riyad when on 16, took full advantage of the lapse, adding 139 runs for the second wicket with Gautum Gambhir (90) and then another 89 for the unbroken fourth wicket with Yuvraj Singh, who made 36 not out.
Gambhir, dropped on 56 by Farhad Reza off Mortaza, also punished the sloppy Bangladeshis with aggressive strokeplay.
Indian captain Mahendra Singh Dhoni praised his team for another clinical win.
"Most of the time we are chasing and it's good that we have done it again. The wicket was flat once again," said Dhoni. "We must keep up the good work and play every game with this rhythm because it's never easy."
Bangladesh skipper Mohammad Ashraful blamed his fielders for the defeat.
"It (dropping catches) is part and parcel of the game but had we taken those catches we would have been in a better position. Raina and Gambhir played well."
The win boosted India's chances of qualifying for the July 6 final. They now have four points after carrying over two points from the first round.
Sri Lanka meet Pakistan in the second match of the Super League on Sunday.
The four remaining teams in the Asia Cup all play each other once at the Super League stage to decide the finalists.
Raina and Gambhir came together after Bangladesh paceman Shahadat Hossain dismissed Robin Uthappa (2) and Rohit Sharman (22) and they took the attack to the Bangladeshi bowlers.
Gambhir hit Mahmudullah over long-on for a six to reach his fifty off just 36 balls. He looked set for his hundred before miscuing a drive off Farhad Reza and was caught at mid-wicket.
Raina took 93 balls for his second one-day hundred. In all he hit eleven boundaries and three sixes during his 107-ball knock.
Earlier, Kapali lifted Bangladesh following a sluggish start after they had won the toss, putting on 112 runs for the sixth wicket with Mahmudullah (26 not out).
Opener Tamim Iqbal, with 55, made an early impression in an otherwise unimpressive start in which Bangladesh lost Nazimuddin (six) and Ashraful (20).
Iqbal kept one end intact and hit seven boundaries during his 67-ball knock, leaving the rest of the work to Kapali.
Kapali added 49 runs for the fifth wicket with Mushfiqur Rahim (22) and then lifted the innings during his 96-ball stand with Mahmudullah.
The 24-year-old Kapali, recalled after a gap of two years earlier this month, smashed Manpreet Gony for two sixes before taking a single to bring up his hundred off just 86 balls.
He smashed ten boundaries and five sixes during his entertaining 96-ball knock before he was caught in the final over.
His previous best one-day score of 89 not out came against the West Indies at Dhaka in 2002.
This was Bangladesh's highest score against India in all one-day matches, beating the previous best of 257-9 at Dhaka in 2004.