Chasing a target of 165 runs, RCB folded up for 134 runs in 19.2 overs.
Leg-spinner Shreyas Gopal led the hosts' charge, sponging up almost the entire RCB top and middle-order to return impressive figures of 4/16 in his four overs.
Pacers Ben Laughlin and Jaydev Unadkat picked up two wickets each.
Earlier, Rahul Tripathi smashed an unbeaten 80 off 58 balls to take Rajastahn a respectable 164/5.
Brief scores:
Rajasthan Royals: 164/5 in 20 overs (Rahul Tripathi 80 n.o.; Umesh Yadav 3/25) vs Royal Challengers Bangalore: 134 in 19.2 overs (AB De Villiers 53; Shreyas Gopal 4/16).
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