Chasing a competitive 158 for win, KKR were in trouble after slumping to 51 for five inside 10 overs. But Ten Doeschate kept a calm head and guided KKR home in exactly 19 overs in Piyush Chawla's company.
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.
KKR's chase, however, started on a horrendous note as they lost their first four wickets inside the 30-run mark.
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.
Young Suryakumar Yadav started brightly with a 17-ball 19 before he was caught by Ravichandran Ashwin off Ravindra Jadeja in the ninth over with KKR scoreboard reading 51 for five in nine overs.
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.
Russell added salt to Mohit and CSK's wounds by finishing off the over with a boundary to score 18 runs off the 16th over.
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.
Earlier, CSK rode on late bursts from skipper Mahendra Singh Dhoni and Dwayne Bravo to post a fighting 157 for four.
With CSK in a spot of bother at 86 for four in 12.3 overs, Dhoni and Bravo joined hands to pull the team out of trouble with an unbeaten 71-run partnership off just 45 balls.
Dhoni finished the innings unbeaten on 35 off 20 balls with the help of three fours and two sixes, while Bravo decorated his unconquered run-a-ball 28-run knock with two boundaries and as many hits over the fence.
Sent into bat, KKR were off to a quick start with the opening pair of Dwayne Smith and Brendon McCullum sharing 37 runs runs off 24 balls.
Smith's 20-run knock off 13 balls was laced with four boundaries before he was caught behind off leg-spinner Chawla (2/26).
McCullum (22 off 19) followed suit as he was struck plumb in front of the wicket by part-time spinner Pathan (1/16) while attempting a reverse sweep.
With CSK in a spot of bother at 49 for two in 6.4 overs, Suresh Raina took the onus on himself to resurrect his side's innings in the company of Du Plessiss.
The duo added 35 runs for the third wicket before Raina was adjudged LBW off Sunil Narine (1/9) in the 12th over with CSK's score reading 84 for three.
With KKR producing a disciplined bowling effort in the middle overs, the CSK batsmen found it difficult to score runs easily.
CSK's problems compounded further when Du Plessiss departed in the 13th over to give Chawla his second wicket of the day.
With runs hard to come by off the spinners, CSK batsmen waited for the pacers to open up.
They finally did when a gutsy Dwayne Bravo opened up against Umesh Yadav and punished the pacer for two fours in the 14th over.
Inspired by Bravo's strokeplay, Dhoni too opened his arms and smashed Russell for two fours to pick up 12 runs in the 15th over.
With overs running out, it was desperate times for CSK batsmen and young Pat Cummins became the victim when Bravo clobbered the pacer for two sixes in the 17th over that yielded 21 runs.
Cummins was once again at the firing line as Dhoni whacked the bowler over deep midwicket boundary for a six in the penultimate over.
Dhoni took Umesh Yadav for task and struck a four and a humongous six off the last ball to finish off the innings in style.
KKR: RV Uthappa†, G Gambhir*, MK Pandey, YK Pathan, Shakib Al Hasan, RN ten Doeschate, SA Yadav, PP Chawla, PJ Cummins, UT Yadav, SP Narine
CSK: DR Smith, BB McCullum, SK Raina, F du Plessis, MS Dhoni*†, RA Jadeja, M Manhas, R Ashwin, IC Pandey, MM Sharma, BW Hilfenhaus.
Chasing a competitive 158 for win, KKR were in trouble after slumping to 51 for five inside 10 overs.
But Ten Doeschate kept a calm head and guided KKR home in exactly 19 overs in Piyush Chawla's company.