The 33-year-old ended his knock unbeaten with 17 maximums (worth a total of 102 runs), another record, and a further 13 fours.
The extraordinary onslaught to reach his century, which came in just 30 deliveries, was four balls quicker than the fastest-recorded ton in limited-overs cricket, hit by Andrew Symonds for Kent against Middlesex in 2004.
He reached the ton after just 8.5 overs, hitting eight boundaries and 11 maximums in 30 deliveries, meaning 98 of his runs came without running.
By contrast, his opening partner, Sri Lanka’s Tillakaratne Dilshan, had laboured to just 17 from 25 balls as RCB reached 123 without loss.
In relative terms Gayle slowed down thereafter, his next 36 balls bringing him a further 75 runs.
Nonetheless, he eased past Brendon McCullum's T20 best of 158 to post the highest individual score in a T20 game as his side scored an astonishing 263 for five, the highest 20-over score seen in domestic cricket. He also passed Graham Napier's record of 16 sixes.
"I'm lost for words myself," said Gayle, speaking at the interval, having been applauded off by the opposition.
"I started really well, I went berserk and it paid off.
"We've got a decent total, and I'm really happy with my performance.
"I'm a bit hungry now, so hopefully I'm going to go and get something to eat."
When asked what he'd had for breakfast to produce such an innings, the left-hander added: "A plain omelette, two pancakes and some hot chocolate."
Gayle capped his day by taking a wicket off the penultimate ball as Bangalore won the match by 130 runs after restricting Pune to 133 for nine.
In the late match, Kings XI Punjab beat Delhi Daredevils by five wickets in Delhi.
David Warner top-scored for the Daredevils with a 36-ball 40 but they could only muster a meagre 120 as Harmeet Singh took three wickets for 24 runs.
Adam Gilchrist’s poor form for Kings XI Punjab continued as he could only make six but they easily chased down the target with three overs to spare.
DA Miller top scored for the Kings XI Punjab with 34 after Mandeep Singh had made 24 off 15 balls.