Fortunes fluctuated like a pendulum in the contest which went to the wire as Piyush Chawla (18) struck a vital six off Anureet Singh to take defending champions closer to the target of 184 and eventually they prevailed with one ball left.
KKR were gasping at 83 for 4 at one stage and the required runrate had shot past 12 with 98 runs required from last eight overs. From there Russell and Yusuf Pathan (29) put on 53 runs from 25 balls for the fifth wicket to turn the match around.
There was never a clear winner as wickets kept falling but KKR kept nearing the target and eventually eight runs were required from the last over. KKR lost two wickets in three balls including that of Chawla, leaving Narine at the crease to score one run from two balls.
The left-hander held his nerve and played a flick shot, did not connect and took the winning run from the legbye to seal his side a thrilling win.
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Earlier, Gambhir had KKR them a brisk start in the power play with 57/1 in the first six overs but introduction of spin put on the brakes.
Left-arm spinner Patel gave away just two runs from his first over, while offie Gurkeerat was tidier with just one run to tighten the proceedings.
As a result Manish Pandey tried to break free in the next over but only to mistime Maxwell and was caught by Patel. Gurkeerat gave the big breakthrough in Gambhir the next over to derail KKR's run chase.