New Zealand skipper Kane Willliamson made just five before he was caught off his gloves fending another fizzing delivery from Bumrah.
The hosts were already well within sight of their target by the time the wickets started falling, however, and it only spared India back-to-back thrashings by 10 wickets.
The thumping victory in the first Test in Wellington did much to ease the pain of New Zealand’s miserable tour of Australia over the New Year and the series sweep underlined how tough it is to beat the Black Caps on home soil.
After the drama of day two, when 16 wickets fell as India stormed back into the match only to be pegged back by the close of play, there was a more subdued atmosphere at an overcast Hagley Oval on Monday.
India resumed on 6-90 with a lead of 97 but Hanuma Vihari, Rishabh Pant, Mohammed Shami and Bumrah all quickly departed and the hosts were soon heading back to the dressing room to pad up.
Trent Boult took 4-28 and Tim Southee grabbed 3-36 as New Zealand’s experienced strike pairing did what they do in home conditions.
India’s final wicket fell when Bumrah charged down the track for a single and was left stranded as Ravindra Jadeja declined the run, a suitably chaotic end to a poor effort from a much-vaunted batting order on New Zealand’s green pitches.