Opting to bat after winning the toss, Bangalore could never get the momentum going their way after losing Chris Gayle in only the second over of the match.
Skipper Virat Kohli (46) and Moses Henriques (44) were the two substantial contributors with the bat.
Bangalore were dealt a body blow early on as young off-break bowler Hanuma Vihari left the dangerous Gayle surprised by having the left-handed West Indian caught behind with his first delivery of the match.
Tillakaratne Dilshan failed for the second time in a row, as the Sri Lankan was cleaned up by Ishant for just five runs.
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Another young batsman in the RCB line-up, Karan Nair, too, did not last long as he was trapped in front by leg-spinner Amit Mishra, which left the visitors in some spot of bother at 42 for three in the eighth over. For the record, Mishra is the second highest wicket-taker in IPL.
There was a partnership between Kohli and Australian all-rounder Henriques that steadied the ship after the three blows with not much on the board.
The RCB skipper had added 43 runs for the fourth wicket with Henriques before his attempted drive through the leg side got a thin edge for Reddy to dive forward a complete a good catch. Kohli hit five fours and a six during his 44-ball knock.
Mayan Agarwal was sent back by Dale Steyn before Thisara Perera dismissed K B Arun Karthik. Henriques' battling innings ended when Ishant had him caught by Cameron White.