Chasing an improbable target of 190 runs, Rajasthan Royals batsmen failed to meet the challenge and were restricted to 143 for seven in 20 overs.
Only captain Rahul Dravid batted sensibly to make 58 with eight fours. The second highest scorer was Stuart Binny who was 20 not out.
Left-arm spinner KP Appanna captured four wickets for 19 runs and Harshal Patel took two for 32.
Earlier, Rajasthan Royals captain Rahul Dravid won the toss and put royal Challengers Bangalore into bat who amassed 189 runs for the loss of only three wickets in the allotted 20 overs.
All credit for this huge total went to a big unbeaten fourth wicket partnership of 122 runs between Tillekaratne Dilshan of Sri Lanka and AB de Villiers of South Africa.
Dilshan remained not out on 76, scored off 58 balls with ten fours and a six while de Villiers smashed five towering sixes and three boundaries in a breezy innings of 59 from just 23 balls.
For Bangalore, Australian left-arm spinner Brad Hogg claimed two wickets for 39.
This match was shown live by Geo Super, the premier sports tv channel of Pakistan