Bangalore are stranded in fourth position tied on 16 points with Sunrisers Hyderabad, who are placed fifth on lower run-rate. Chennai Super Kings are at the top with 20 points followed by Mumbai Indians and Rajasthan Royals, on 18.
Sunil Narine produced one of the best spells of spin bowling this tournament taking four wickets and helping his team restrict Royal Challengers to a meagre score of 115 for nine.
Jacques Kallis (41) played the perfect anchor role taking his team to a score of 116 for five in 19.2 overs.
Kolkata, though, didn't have it all easy as they lost Manvinder Bisla for naught in only the second ball of the innings.
Gautam Gambhir (14) again failed to make a big contribution and was dismissed by pacer Vinay Kumar.
Yusuf Pathan settled the nerves with a couple of big hits but his stay was shortlived as he fell prey to wily spinner Murali Kartik.
Kallis along with Manoj Tiwary (24) slowly but surely edged their way towards the target.
Both though fell in successive overs but it was all a bit too late for Bangalore as Ryan ten Doeschate (11 n.o) and Rajat Bhatia (3 n.o) added the finishing touches.
Earlier, Bangalore put in to bat, lost Cheteshwar Pujara (5) early. Chris Gayle (33 off 36) played an uncharacteristically slow innings, hitting just one four and a six.
Virat Kohli (17) failed to reproduce the heroics of his last match, where he scored a brilliant 99, and was castled by Kallis.
AB de Villiers was the most impressive of Bangalore batsmen scoring 28 off 22 balls but in trying to reverse sweep Lakhmipathy Balaji, he edged one to Bisla.
The South African's wicket opened the floodgates for the Knight Riders as they took the last six wickets giving away just 17 runs.