It was David Warner's batting and astute captaincy complemented by some inspirational death overs bowling by Mustafizur Rahaman (1/37 in 4 overs) and Bhuvneshwar Kumar (0/25 in 4 overs) that clinched the issue.
Warner, who hit 68, finished second in run-getters' list with 848 runs.
The turning point certainly would be the 24 runs that Ben Cutting (39 no and 2/35) got in the final over off Shane Watson's bowling during Sunrisers innings and then came back to dismiss a rampaging Gayle.
With 18 needed off last over, Bhuvneshwar, who bowled 13 dot balls gave only 9 runs. As the last ball was delivered, skipper Warner's joy knew no bounds with the entire team and dug-out joining him in wild celebrations.
Gayle (76 off 38 balls) and skipper Kohli (54 off 35 balls) had a scintillating opening stand of 114 in 10.3 overs as it looked like a cakewalk for the home team.
But in the end, Kohli was the tragic hero once again after the WorldT20 in a tournament that will be remembered for his exploits.
He finished the tournament with an astounding 973 runs at an average of 81.08 and and equally impressive strike-rate of 152.03. He hit an unbelievable four hundreds and seven half-centuries, not to forget 83 boundaries and a staggering 38 sixes.
Once the duo were back in quick succession, it depended AB de Villiers (5), who had one of his rare failures as Sunrisers came back into the match.
KL Rahul was done in by a slow off-cutter from Cutting and Shane Watson found it hard to get the big shots going as Mustafizur accounted for him.
Stuart Binny hit Mustafizur down the ground for a six as the equation came down to 37 from 3 overs.
But Bhuvneshwar bowled a brilliant 18th over keeping everything in the blockhole as only 7 came off the over.
RCB 30 were needed off last two overs as Binny (9) was run-out off the first delivery of the 19th over bowled by Mustafizur. Sachin Baby hit six off the last ball as RCB's requirement of final over was 18 runs but Bhuvneshwar kept his cool to win the match for Sunrisers.
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