Chennai and Mumbai share an old rivalry, with both teams winning five titles each in the T20 tournament that began in 2008.
The hosts fielded first and their bowlers justified Gaikwad’s decision as fast bowler Khaleel Ahmed rattled the Mumbai top-order, including getting former skipper Rohit Sharma out for a duck in the first over.
Left-arm quick Khaleel bowled South African Ryan Rickelton for 13 as he under-edged a delivery onto his stumps.
Ahmad took over from Khaleel and turned on the heat with his left-arm wrist spin as he struck twice in one over and removed the dangerous Tilak Varma for 31.
Wickets kept tumbling but Deepak Chahar hit a late cameo of 28 to give Chennai something to think about.
Opener Ravindra put on 67 runs for the second wicket with Gaikwad as Chennai appeared set to cruise to their target.
But left-arm wrist spinner Vignesh Puthur took three wickets on his IPL debut, despite never having even played state cricket before, making his presence felt by dismissing Gaikwad, Shivam Dube and Deepak Hooda - all India internationals.
Chennai wobbled when spinner Will Jacks bowled fellow Englishman Sam Curran for four, but Ravindra kept calm and with Ravindra Jadeja, who was run out for 17 in the penultimate over, helped the team get over the line.
Dhoni failed to get off the mark from the two balls he faced, but watched from the non-striker’s end as Ravindra smashed his New Zealand teammate Mitchell Santner into the stands to complete the win.