The Sunrisers had overcome a gentle start, reaching just 62 for three wickets after 10.2 overs, to set a competitive total of 161 for five.
Cameron White (52) and Thisara Perera (40) gave the innings much-needed impetus, while RP Singh bowled economically for three wickets.
It looked as if Chris Gayle would be key to the Challengers' response, and when he fell for 13 to leave RCB at 47 for two, the Sunrisers had cause for optimism.
But Kohli's virtuoso innings, which included 11 fours and four maximums, swiftly took the game away from them.
Royal Challengers Bangalore eventually completed victory with 14 balls to spare.
In the late game, the Mumbai Indians overcame the loss of two early wickets to post an impressive 209 for five, which led to a to a 44-run win over the Delhi Daredevils.
Dinesh Karthik the standout performer with 86 runs from 48 balls with Rohit Sharma making 74, leading a superb recovery after Ricky Ponting went for a duck and Sachin Tendulkar followed the over after having been run out.
Decent knocks from Dave Warner (61) and Manprit Juneja (49) were not enough for the Daredevils, who could only reach 165 for nine in their 20 overs.
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