Opting to bowl after skipper Rohit Sharma won the toss, Mumbai Indians had KKR on the mat at 31 for five in the seventh over.
However, a 56-run partnership for the sixth wicket between Suryakumar Yadav (31) and Ishank Jaggi (28) steadied KKR's sinking ship, before leg spinner Karn Sharma struck for the fourth time on the night.
Sharma returned excellent figures of 4/16 from four overs, while Jasprit Bumrah had equally great figures of 3/7 in three overs, as KKR were all out in 18.5 overs.
The 29-year-old Sharma sent back Sunil Narine, Robin Uthappa, KKR captain Gautam Gambhir and Ishank Jaggi at the M Chinnaswami Stadium.
Jaggi's dismissal in the 15th came as a relief for MI as the batsman had whipped Lasith Malinga for two boundaries in the previous over and was starting to look threatening.
Suryakumar Yadav struck two boundaries and a six while facing 25 balls.
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