Needing 10 runs of the final over, Vinay Kumar picked up the crucial wickets of dangerman Dinesh Karthik (60) and Ambati Rayudu in successive balls to snatch the win for RCB.
Kieron Pollard gave a late scare to the hosts when he hit Vinay Kumar straight for a boundary to bring down the equation to four off the last ball, but the RCB bowler kept his cool and gave away just one run to hand his side a winning start.
Earlier, after a relatively slow start, Gayle upped his tempo and scored his 92 off just 58 balls with the help of 11 fours and five towering sixes to take RCB past the 150-mark.
Chasing the challenging total, Mumbai made a steady start with skipper Ricky Ponting and Sachin Tendulkar putting on 52 runs for the opening wicket before both departed quickly.
While Ponting made a quiet 28 off 33 balls, Tendulkar was the aggressor among the duo scoring his 23 runs off just 19 balls with the help of four fours, two of which came of successive balls off Mutttiah Muralitharan's opening over.
Tendulkar did not take any undue risk during his knock and seemed eager to stay there till the end. But his innings was cut short when he fell prey to a close run out.
Ten runs later Mumbai slumped to 62 for two when Ponting was stumped by K B Arun Karthik off left-arm spinner Murali Kartik in the 10th over.
Talented Rohit Sharma (11) wasted yet another opportunity as the Mumbai batsman, going for a huge heave over midwicket off R Vinay Kumar, missed a straight ball which crashed on to his off stump.
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