Mayank smashed Munaf Patel for 24 runs in the innings' last over, which included two sixes and as many fours.
In all, he hit six fours and four sixes after the hosts lost most of their big guns, including Chris Gayle and A B de Villiers cheaply.
Mayank came out to bat when RCB were precariously placed, having lost four wickets with less than 100 on the board.
At the start however, Munaf did not disappoint captain Harbhajan Singh who hoped to get early wickets by exploiting a slightly greenish pitch, as he struck two crucial blows for Mumbai Indians, dismissing Gayle for just six and running out host captain Virat Kohli for three.
In his first over Lasith Malinga almost had Saurabh Tiwary caught at deep extra cover but fortunately for the batsman, the ball landed safely between two fielders.
Tiwary helped Bangalore recover from a poor start before being dismissed for 21. Suddenly, the hosts were in trouble at 47 for three by the seventh over.
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After losing three wickets, Dilshan and AB de Villiers were involved in a 40-run partnership in 29 balls before Kieron Pollard removed the South African wicketkeeper-batsman for 14.
RCB posted their 100 in the 15th over.
Agarwal cut loose in the 16th over and hammered 11 of the 15 runs conceded by RP Singh. Agarwal hammered a length ball to deep backward point for a four and then lofted one over long-off for a maximum.
However, RP put an end to the 46-run stand for the fifth wicket by bowling out the Sri Lankan opener for 47 (50 balls 4x4 and 6x1) in the 17th over.