Jadeja scalped three wickets for 29 runs and rattled the Mumbai Indians top order after the home side elected to bat at the Wankhede Stadium.
But captain Rohit Sharma's (39 not out) late flourish and Harbhajan Singh's (25 not out) useful contribution helped Mumbai post a challenging total with the duo sharing 52 runs from just 4.9 overs for the unfinished sixth wicket.
Harbhajan hit two fours and two sixes in his unbeaten 11-ball knock while Rohit struck three fours and a six in his 30-ball unbeaten innings. The duo took 19 runs off the last over bowled by Ben Laughlin.
Mumbai openers started slow and scored just 21 runs in the first five overs. Sachin Tendulkar (15) tried to up the tempo by scoring 11 runs off Mohit Sharma in the sixth over with a six and a four but the veteran was trapped leg before by Jadeja in the next over.
More From This Section
After Tendulkar's dismissal, with 40 runs on board, Mumbai Indians started losing wickets in a heap.
Tendulkar's opening partner Dwayne Smith (22) departed in the next over when he was caught and bowled by fellow West Indian Dwayne Bravo. West Indian all-rounder Kieron Pollard (1) was promoted up the order but could not contribute much.
Mumbai was then struggling at 82 for five before skipper Sharma and Harbhajan started the repair job in the 16th over.
The Chennai bowling attack was disciplined till Laughlin conceded 19 runs in the last over. Laughlin leaked 46 runs in his four overs without picking up a wicket. Off-spinner R Aswhin and Bravo grabbed a wicket each.