Coming on to bowl the 19th over, Mohit picked up three wickets - Ambati Raydu, dangerman Kieron Pollard (12) and Harbhajan Singh - to prevent a late burst from Mumbai batsmen.
Apart from Mohit (4/14), Ben Hilfenhaus (2/39) picked up two wickets for the Chennai utfit.
Mumbai's innings mainly revolved around captain Rohit Sharma and Correy Anderson. While Rohit made 50 off 41 balls with the help of three fours and two sixes, big-hitting Anderson scored 39 off 31 balls.
But once the duo departed their innings fell apart as Mumbai could manage just 33 runs off the last five overs for the loss of five wickets.
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Electing to bat, Mumbai did not have the best of starts as they lost Mike Hussey (1) and Aditya Tare (23) early.
Hussey's poor form in the tournament continued as he was bowled by fellow Australian Hilfenhaus in the second over.
An over later, Tare perished in search of a big hit, caught by Suresh Raina off Sharma. He struck four boundaries during his 19-ball knock.
Together with Rohit, Anderson shared 84 runs off 64 deliveries for the third wicket before a direct hit from Ravichandran Ashwin cut short his stay.
After failing in the first two matches, Rohit finally came to his fore and together with Anderson played sensibly to lay the platform for the score.
Rohit started cautiously before opening up but he departed just after reaching his fifty, caught by Dwayne Smith off Hilfenhaus in the 18th over.