Opting to field first at Sardar Patel stadium, Motera, Royal Challengers Bangalore struck early with Harshal Patel removing the Orange cap holder Ajinkya Rahane for 18 with a slower delivery.
Rajasthan Royals captain Shane Watson played some eye-pleasing shots but perished in the sixth over to Yuzvendra Chahal.
Smart piece of work in the outfield by Harshal Patel found Karun Nair short of his crease as RR lost their third wicket inside the first 10 overs.
Mitchell Starc was the pick of the bowlers for RCB as the Australian claimed three wickets for just 22 runs in his four overs as RR managed to score 130 for 9 in their 20 overs.
A flurry of wickets further dented Rajasthan Royals progress even though Steven Smith tired his best to inject some life in to the RR innings with a 28-ball 31-run knock.
Poor shot selections from Deepak Hooda and Sanju Samson meant that Rajasthan Royals found themselves in trouble. While Hooda was removed by Iqbal Abdulla, Samson gifted his wicket to Yuzvendra Chahal.
Virat Kohli and AB de Villiers combined for a match-winning unbeaten partnership of 98 runs for the second wicket.
In chase of 131, RCB lost Chris Gayle early for 20 runs to Shane Watson.
Skipper Virat Kohli led the chase and remained unbeaten on 62 off 46 balls with the help of one four and three sixes.
AB de Villiers played second fiddle to perfection and scored 47 not out off 34 balls as RCB cantered home with 23 balls to spare and nine wickets in hand.