Chasing a competitive 158 for win, KKR were in trouble after slumping to 51 for five inside 10 overs.
But Russell (58 off 25) and Ten Doeschate shared match-winning 80 runs for the sixth wicket off just 42 balls to keep KKR afloat.
After Russell's dismissal, Ten Doeshchate took the onus on himself to guide KKR home and managed to achieve that with six balls to spare.
Left-arm pacer Ashish Nehra (4/21) was the wrecker in chief for KKR. He accounted for the wickets of KKR skipper Gautam Gambhir, Manish Pandey and Manvinder Bisla in quick succession to rattle CSK.
In fact, Nehra was on the verge of a hat-trick as he dismissed Gambhir and Pandey in consecutive balls in the third over.
Yusuf Pathan too failed to sparkle as he edged a Mohit Sharma delivery to Faf du Plessiss in the first slip in the fourth over.
But Ten Doeshchate and Russell had other plans as they started cautiously to build up the chase before opening up.
Russell was the aggressive among the duo as he laced his knock with four boundaries and five huge sixes. Ten Doeschate, on the other hand, played the second fiddle and struck three fours and two hits over the fence during his unbeaten knock.
Russell was at his attacking best as he struck two massive sixes of Mohit Sharma in the 16th over to not only bring KKR closer but also bring up his half century in style.
Just when it seemed Russell's pyrotechnics would take the game away from CSK, Nehra cleaned up the West Indian with a gem of an yorker to pick up his fourth wicket of the day and bring his side back into the game.
