Needing 29 runs off the last over, Rinku whacked left-arm pacer Yash Dayal for five maximums on the trot to register a last-ball sensational victory.
Rashid Khan led from the front and returned with impressive figures of 3 for 37, while Alzarri Joseph (2/27) picked up two wickets, but all their efforts went in vain.
Venkatesh Iyer made 83 off 40 balls for KKR while skipper Nitish Rana played a fine 29-ball 45-run knock.
Rinku played the knock of his life and struck one four and as many as six hits over the fence to seal a famous win for KKR.
Earlier, electing to bat, GT rode on Sai Sudharsan and Vijay Shankar’s fifties to post a mammoth 204 for four.
Hardik Pandya missed the game as he is unwell and in his place Rashid led GT.
Sudharsan made a 38-ball 53 while Shankar scored an unbeaten 63 off just 24 balls.
Besides Sudharsan and Shankar, opener Shubman Gill made 39.
For KKR, Sunil Narine picked up three wickets by giving away 33 runs.
(With inputs from PTI)