Set 207 for victory, five-time winners Mumbai finished on 186-6 even though Rohit raised his ton in 61 balls at his home in Wankhede Stadium.
Skipper Ruturaj Gaikwad and the in-form Shivam Dube powered Chennai, who won their fifth title last year, to 206-4.
Gaikwad hit 69 and Dube smashed an unbeaten 66 before warhorse M.S. Dhoni smashed three successive sixes in the 20th over to take Chennai past 200.
Dhoni came in to bat with four balls left and scored 20. He smashed Mumbai skipper Hardik Pandya for three sixes and finished with a two to end a 26-run over.
"Our young wicketkeeper scoring three sixes down the order helped a lot and I think that was the difference," Gaikwad said of the 42-year-old Dhoni.
Sri Lanka quick Matheesha Pathirana then took four wickets to push Mumbai to their fourth loss of the season and Gaikwad said he bowled "exceptionally well and nailed those yorkers".
The two teams are on contrasting runs after changes of guard this season.
Pandya replaced Rohit as Mumbai captain while Dhoni surprisingly handed over the Chennai leadership to Gaikwad.
Gaikwad had his fourth win as captain after he set the pace for his team with his 40-ball knock laced with five fours and five sixes.
He put on 90 runs with Dube before falling to Pandya, but Dube and then Dhoni's cameo ensured Chennai finished strongly.
Mumbai started well with Rohit and Ishan Kishan putting on 70 runs for the first wicket before Pathirana hit back.
Salt and Starc
Pathirana, known "Baby Malinga" for his slinging action similar to former Sri Lankan quick Lasith Malinga, sent back Kishan and then Suryakumar Yadav, for his second duck this season, in the space of three balls.
He later dismissed Tilak Varma for 31 as Rohit attempted to keep up the charge in his 63-ball knock and his second IPL ton.
Pathirana was named man of the match and Pandya said the Sri Lankan "was the difference".
Tushar Deshpande got Pandya out and the home crowd cheered in another sign of growing unpopularity of Mumbai's choice of captain.
In the first match of the day, Phil Salt's rapid 89 and three wickets for Mitchell Starc helped Kolkata Knight Riders race to a crushing eight-wicket win over Lucknow Super Giants.
Starc's 3-28 kept Lucknow down to 161-7 at Kolkata's Eden Gardens, with the other Knight Riders' bowlers putting in disciplined performances after their side elected to field first.
The Australian left-arm quick became the most expensive buy in IPL history after Kolkata shelled out $2.98 million for his services.
Opener Salt then steered the two-time IPL winners to their target in 15.4 overs for their fourth victory in five matches this season.
The English wicketkeeper-batsman put on 120 runs with skipper Shreyas Iyer, who made 38, smashing 14 fours and three sixes in his 47-ball knock.
