Chasing a modest 141, MI lost wickets at regular intervals after being 60 for one to be shot out for 108 in 19.1 overs, their second lowest total of the season after the paltry 92 made against Delhi Daredevils at this venue.
West Indian off-spinner Sunil Narine was unplayable and pushed MI to the brink with a superb haul of four for 15.
Narine was well-supported by Laxmipathy Balaji (2 for 11) and Jacques Kallis (2 for 42), while left arm spinners Shakib Al Hasan and Iqbal Abdulla too did their bit with a wicket each.
MI batsmen made a hash of what appeared to be a gettable score at the Wankhede Stadium and again the dismissal of their icon Sachin Tendulkar for 27 in the 11th over triggered a sharp collapse, which saw the home team lose their last eight wickets for just 48 runs.
The MI batsmen struggled against the varied KKR attack on a wicket that possessed no devil like in the past but provided some appreciable bounce to the spinners.
The victory helped KKR to take the second spot behind table leaders Delhi Daredevils with 19 points, while MI remained third on 18 points ahead of their final game against Rajasthan Royals at Jaipur on May 20.
KKR will face Pune Warriors in their final league game at Pune on Saturday.
Apart from Tendulkar, who hit three fours and a six in 24 balls, Dinesh Kartik (21), Rohit Sharma (12) and Ambati Rayudu (11) got starts but failed to bring Mumbai to the finishing line.
Earlier, Rudra Pratap Singh bagged two wickets in as many balls in his first over as MI restricted KKR to a modest 140 for seven.