Rayudu smashed an unbeaten 81 off 54 balls while Pollard remained not out on 52 off 31 as Mumbai Indians chased down the target of 172 with two balls to spare after staring down the barrel at 51 for five in the ninth over.
Pollard smashed Gayle for a six and two fours to seal the match for Mumbai and keep their chances of qualifying for the playoffs alive.
Pollard and Rayudu hit nine runs in the penultimate over off Zaheer, leaving Mumbai to score 14 in last over.
The nightmare of not getting good starts haunted MI yet again when they lost three early wickets by the fourth over.
In Image: Mumbai Indians' Ambati Rayudu, second right and teammates celebrate winning their Indian Premier League (IPL) match against Royal Challengers Bangalore
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