While de Villiers made 83 off 46 balls with the help of six boundaries and two sixes, Kohli's 80 came off 63 deliveries during which he struck seven fours and two hits over the fence.
Thisarra Perera (3/34) was the pick of the bowlers for Pune, picking up all the three wickets to fall.
Sent into bat, RCB had a relatively quiet start, stitching 27 runs off 22 balls for the opening wicket before KL Rahul (7) became the first victim.
But the dismissal brought together two most destructive batsmen of modern day cricket in Kohli and De Villiers and as expected the duo played fearless cricket and displayed a vast array of shots to put together 155 runs off just 95 balls for the second wicket.
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As ususal De Villiers was at his attacking best from the word go while Kohli played the second fiddle.
De Villiers and Kohli shared their fourth half-century stand this season with a two off Rajat Bhatia in 9.5 overs.
De Villiers didn't let Murugan Ashwin settle down and smashed the bowler for two boundaries in his next over.
Kohli and De Villiers brought up their third century stand this season in the 15th over.
An over later Kohli got a lifeline when Ankit Sharma dropped a skier off Ravichandran Ashwin.
It was all Kohli and De Villiers show till the last over when both the batsmen perished in sucessive balls in search of big shots but note before setting the platform for the huge total.