Opting to field, KKR restricted RCB to 115 for nine, and then chased down the modest target with four balls to spare at the JSCA International Stadium Complex.
Narine finished with impressive figures of four for 22 off his four overs and there were two wickets apiece for Jacques Kallis and Lakshmipathy Balaji.
Kallis also top-scored for the 'hosts', playing a responsible knock of 41 off 45 balls. Manoj Tiwary made 24 off 27 balls.
Gambhir and Kallis steadied KKR with a 31-run partnership for the second wicket.
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Playing according to the situation, the two experienced pros relied on the ones and twos, besides hitting boundaries occasionally.
In the fourth over bowled by Abhimanyu Mithun, the KKR skipper scored three successive fours -- all through the off-side, with the first one almost going all the way for a maximum.
However, what was turning out to be a promising stand, was cut short as R Vinay Kumar induced a thick outside edge off the blade of Gambhir for Chris Gayle, the lone slip fielder, to pounce on to the offering.
The all-rounder from Baroda then guided Jaydev Unadkat for a boundary with an upper cut.
But, as had been the case in the past, Pathan again got out after getting a start, trapped in front while going for a sweep shot against Kartik.