Courtesy Kohli's blistering 29-ball-56, RCB posted 106 for two in only eight overs in a match curtailed by rain and then restricted CSK to 82 for six.
RCB finished their league engagements with 18 points and will now hope that KKR turn out to be 'party poopers' for Hyderabad Sunrisers which will ensure their passage in play-offs by virtue of better net run-rate.
Zaheer (4/17), playing only his second match since comeback dealt twin blows removing the two in-form men in Mike Hussey (6) and Suresh Raina (0) off successive deliveries.
While Hussey edged one that kicked up from back of the length with glovesman Lokesh Rahul taking a good catch, Raina went for a slog shot only to offer a skier for Rudra Pratap Singh. Two wickets giving away only three runs clinched it decisively in favour of RCB.
The third wicket came in the fourth over when Dwayne Bravo top edged one to Saurabh Tiwary in the deep third man region.
CSK skipper Mahendra Singh Dhoni came in with 78 required off four overs but it wasn't one of those days when impossible could have been achieved.
Earlier, spectacular hitting by Kohli helped RCB post an imposing target in a shortened game. He led from the front smashing an unbeaten half-century.
Kohli hit six fours and four sixes in his 29-ball knock.
He added 67 runs with Chris Gayle (28, 13 balls, 4x6) for the opening stand.
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