Moreover, Kolkata posted the season's highest total, 232 for two, after sensational knocks from Shubman Gill (75 off 45) and Andre Russell (80 not out off 40).
The much-needed win keeps KKR alive in the tournament as they now have 10 points from 12 matches. Mumbai remain in the third spot with 14 points from 12 games.
At 58 for four, Mumbai were down and out but Hardik Pandya reignited their hopes with a breathtaking 91 off 34 balls. In the end, Pandya's dismissal in the 18th over sealed the game in KKR's favour as Mumbai ended at 198 for seven. The Indian all-rounder's cracking innings comprised nine sixes and six fours.
Staring at elimination, the embattled KKR got off to a fiery start with Shubman Gill (76) and Chris Lynn (54) putting on a 96-run opening stand, their highest this season, after Rohit Sharma opted to bowl in his 100th match as captain.
Russell hammered six fours and eight sixes including one off the last ball after he denied a couple of singles to skipper Dinesh Karthik in the last over as KKR creamed 75 runs from the last five overs and scored 135 in the final 10.
Fielding let down Mumbai Indians big time with both Lynn and Russell dropped early in their innings by Kieron Pollard and Evin Lewis respectively.
On a belter of a track, KKR openers got off to a sensational start and survived the powerplay without losing a wicket for their highest opening stand -- 96 -- this season.
Slow to start with, Lynn was 18 off 15 balls when Kieron Pollard spilt a chance from the Aussie at mid-off. Lynn took off from there on, hammering the spin duo of Krunal Pandya and Chahar to race to his fourth IPL fifty this season off just 27 balls.