Kohli, who got two reprieves during his sensational knock, along with A B de Villiers put on 94 runs off just 40 balls for the fourth wicket to set the hosts a daunting target at the Feroz Shah Kotla.
An innovative De Villiers used the long handle to great effect and played a 17-ball 32-run cameo to further the visitors' cause.
Sent into bat, RCB did not have the best of starts as they lost their openers, which included the dangerous Chris Gayle, inside the fifth over.
Gayle departed without inflicting much damage as he played on to his stumps an Irfan Pathan delivery in the second over.
Cheteshwar Pujara scored a run-a-ball 17 with the help of three boundaries before he was cleaned up by Siddharth Kaul.
Kohli's first life came in the third over when he edged a Morne Morkel delivery to Kedar Jadhav behind the stumps which, much to the dismay of home fans, turned out to be a no ball.
The RCB captain was once again at the receiving end of God's favour as Virender Sehwag dropped him inside the circle off Kaul.
Kohli and Moises Henriques thereafter added 57 runs off 50 balls for the third wicket to stabilize RCB's innings.
Henriques scored 26 off 22 balls with the help of three boundaries before Shahbaz Nadeem had the batsman, caught off his own bowling.
Kohli and de Villiers than upped the ante and stitched a 50-run partnership in just 27 balls.
De Villiers started the onslaught by clobbering Morkel for a huge six over the fine-leg boundary and then Kohli smashed the bowler for two fours to pick up 18 runs off the 17th over.