This win took the visitors to second place in the table with 19 points while Mumbai are just one point behind with both teams left with a single match.
The hosts chasing a moderate total were immediately put under pressure by disciplined bowling by Kolkata. South African Herchelle Gibbs was the first one to go, trapped in front of the wicket by Iqbal Abdulla.
Sachin Tendulkar (27) and Dinesh Karthik (20) put on a 46-run stand too fell in close succession to leave Mumbai in a spot of bother with the score on 66 for three in the 13th over.
In Image: Kolkata Knight Riders Sunil Narine celebrates the dismissal of Mumbai Indians' Rohit Sharma