After RCB posted 158 runs for the loss of six wickets, KKR batsmen came down with a purpose and reached 159 runs by losing just four wickets.
Narine played a memorable knock as he scored the fastest half-century to demolish the opponent attack.
He hit six boundaries and four sixes in his knock.
He got strong support from the other end from Chris Lynn who hammered 22-ball 50.
Lynn was destructive in his approach as he sent four sixes outside the park while adding five boundaries with the willow.
Narine, who ha opening for KKR quite often in the tournament, came out as surprise as he ruthlessly destroyed the opposition attack, giving less chance to skipper Virat Kohli to think a strategy against him.
After the openers departed, Colin de Grandhomme scored 31 while Gautam Gambhir contributed 14 runs.
Pawan Negi took two wickets for RCB.
Earlier, Travis Head remained 75 not out as RCB added 158 runs on the scorecard.
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