Daredevils were blown away by Gayle's carnage as the Jamaican struck a brilliant unbeaten 62-ball 128, his first century of the season.
Gayle and skipper Virat Kohli (73 not out) added 204-run stand for the second wicket, the highest for any wicket this season, which took Royal Challengers to a massive 215 for one in 20 overs.
Daredevils, who had already qualified for the play-off, gave a tough fight but were restricted to 194 for nine in 20 overs after Ross Taylor struck 26-ball 55, for his first half-century of the season.
In Image: Chris Gayle, right, and Virat Kohli of Royal Challengers Bangalore walk back after their unbeaten 204 run second-wicket partnership
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