Chasing a target of 172, CSK top-order batsmen chipped with handy contributions but they wobbled towards the end before Jadeja pulled off the win with an 8-ball 22 which was studded with two fours and as many sixes to help his side reach 172 for 8 in 20 overs.
Faf du Plessis (44), Ruturaj Gaikwad (40), and Moeen Ali (32) were the other contributors.
Earlier, KKR scored 171 for six after opting to bat. Rahul Tripathi made 45 off 33 balls, while useful contributions also came from Nitish Rana (37 not out) and Dinesh Karthik (26).
India pacer Shardul Thakur was one of the best bowlers for CSK in the game, returning impressive figures of 2/20 in his quota of four overs. Josh Hazlewood also picked up two wickets, including that of KKR skipper Eoin Morgan.
Brief scores:
Kolkata Knight Riders: 171/6 in 20 overs (Rahul Tripathi 45, Nitish Rana 37 not out, Dinesh Karthik 26; Shardul Thakur 2/20).
Chennai Super Kings: 172 for 8 in 20 overs (Faf du Plessis 44, Ruturaj Gaikwad 40, Ravindra Jadeja 22; Sunil Narine 3/41).
Visit news.dtnext.in to explore our interactive epaper!
Download the DT Next app for more exciting features!
Click here for iOS
Click here for Android