Chasing a paltry 120, the Super Kings found themselves on a tight corner when they were redused to 89 for six in the 17th over.
But Jadeja (36 off 14) meant business and used his long handle to great effect to wrap up the issue for CSK. He shared an unbeaten 35-run partnership with Dwayne Bravo (7) to guide CSK home.
Apart from Jadeja, Mike Hussey (40 off 51) played a sensible innings at the top to keep CSK in the hunt even thought wickets kept falling at the other end.
Jadeja got a huge reprieve when Yusuf Pathan dropped him at the square leg boundary as he continued his assault with three boundaries in Kallis' penultimate over that reduced the equation to two runs from the last over.
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Jadeja was in no mood to relent even though the game was under their control. He pulled Pathan over midwicket boundary for another six to help the Super Kings wrap up the issue with five balls to spare.
Narine gave KKR breakthrough in the fifth over, dismissing Ashwin while Senanayake, who opened the proceedings with Balaji, ran through his four overs and gave the team their second wicket in the form of Murali Vijay (2).