Narine smashed a 17-ball 54 – including six fours and four sixes – as Kolkata reached the 159-run target in 15.1 overs to win by six wickets late on Sunday.
Narine and Australian Chris Lynn put together a 105-run opening partnership in the first six overs of Sunday's game. Lynn needed 22 balls to make his 50 at Bangalore's M. Chinnaswamy Stadium.
He was outdone by Narine who, despite being better known for his off-spin bowling, matched Yusuf Pathan's 15-ball half-ton for Kolkata in 2014.
"I'm surprised too. Lynn just said keep your eyes on the ball, keep focused and swing at it. I try to keep it simple," Narine said.
"I'll hopefully get used to the expectations but it really was a team effort. Umesh's (Umesh Yadav) wickets early especially were key and I'm thankful for it," added Narine.
Bangalore's batting again faltered with big-hitter Chris Gayle, who fell for a golden duck in his 100th IPL game, skipper Virat Kohli and AB de Villiers managing just 15 runs between them.
Australia's Travis Head hit an unbeaten 47-ball 75 to take Bangalore to 158-6 in 20 overs. Kolkata paceman Yadav took three wickets while man-of-the-match Narine bagged two.
Gautam Gambhir-led Kolkata lie second in the eight-team table, with bottom-placed Bangalore already out of the play-off race in the cash-rich league.