Rohit top-scored for MI with 67 from 48 balls with the help of six fours and three sixes, but it was Kiwi left-arm spinner Mitchell Santner who starred with the ball for CSK with brilliant figures of 2 for 13 from his four overs.
Sent in to bat by stand-in captain Suresh Raina after Mahendra Singh Dhoni was ruled out of the match due to fever, MI couldn't capitalise on a good start, faltering against some accurate bowling by the home team.
From 103 for two in 13 overs, MI could only muster 52 runs in the final seven overs.
The big-hitting Hardik Pandya (23 not out off 18 balls, 1x4, 1x6) and Kieron Pollard (13 off 12 balls, 2x4s) couldn't do much damage but still managed to get MI past the 150-run mark.
Rohit led from the front with a typically elegant half-century, his first of the season, during which he hit some big sixes and looked in control for the most part. He was holed out to Murali Vijay at long-on off Santner, who bowled a brilliant spell.
Krunal Pandya pushed up the order in a bid to speed up the scoring rate, fell for just one run, caught by Santner in the deep off Imran Tahir's bowling.
West Indies power-hitter Evin Lewis (32) added 75 runs with Rohit for the second wicket and took the attack to the CSK bowlers.
The fast-improving Deepak Chahar got the first wicket for CSK in the form of dangerous Quinton de Kock (15) with a slower ball.
Earlier, CSK won the toss and elected to field but were dealt a big blow ahead of the match with captain Dhoni missing out due to fever. Also, Faf du Plessis and Ravindra Jadeja missed out and Santner, Murali Vijay and Dhruv Shorey came in.