Zimbabwe made five changes for the third and final ODI, but it made no difference as they were bowled out for 123.
India required less than 22 overs to chase a target of 124, as KL Rahul made an unbeaten 63 and Faiz Fazal marked his international debut with 55 not out.
The two teams begin a three-match Twenty20 international series at the same venue on Saturday.
Bumrah’s four-wicket haul saw him named man of the match for the final game of the series.
Second four-wicket haul for Jasprit Bumrah against Zimbabwe in the ongoing series #ZIMvIND pic.twitter.com/N4aJsAJbDP
— BCCI (@BCCI) June 15, 2016
Meanwhile, Rahul was named as the man of the series for his efforts with the bat.
It's @klrahul11 who takes the Player of the Series award for his 196 runs at an average of 196.00 #ZIMvIND pic.twitter.com/vMEwvUF3Qt
— ICC (@ICC) June 15, 2016
The inexperienced Indians were ruthless in victory and in securing the whitewash captain MS Dhoni moved level with Allan Border with the joint-second highest ODI wins as captain.
Most ODI wins as captain
— Mohandas Menon (@mohanstatsman) June 15, 2016
165 - Ricky Ponting
107 - Allan Border/MS Dhoni#ZimvInd