Jadeja was named Player of the Match for his 3/20 against MI.
MS Dhoni had won the toss and chosen to bowl first and though initially Rohit Sharma (21) and Ishan Kishan (32) gave a flying start to MI, Ravindra Jadeja removed the dangerous Ishan Kishan, Cameron Green (12) and Tilak Varma (22).
His 3/20 helped CSK keep MI to 157/8 in 20 overs with Tushar Deshpande and Mitchell Santner also taking two wickets.
India legend Sunil Gavaskar praised the CSK all-rounder for his performance and compared his fearlessness with his captain MS Dhoni.
"Like his captain, Jadeja is absolutely fearless. Green's catch is like making a possibility out of the improbable. No matter how much you praise this player, it is less," Gavaskar told Star Sports.
"MS Dhoni made excellent use of Santner and Jadeja against Mumbai Indians batters. He knew that on such wickets these two can turn the tide, and that is why he showed more confidence in them," said Shastri.
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In reply, Jason Behrendorff removed Devon Conway for a duck, but Ajinkya Rahane hammered the MI bowlers reaching his half-century in 19 balls and finishing on 61 off 27 deliveries with 7 fours and 3 sixes.
His assault was enough for CSK to gain an advantage and Shivam Dube (28), Ruturaj Gaikwad (40*) and Ambati Rayudu (20*) ensured the yellow army won the match by 7 wickets and 11 balls to spare.
The defeat meant that five-time champions MI have now lost both their matches so far in this season.
MI will now face Delhi Capitals in an away game on Tuesday (April 11), while CSK take on Rajasthan Royals at home in Chennai on Wednesday (April 12).
(Star Sports inputs)