Kohli top-scored for Bangalore with 35 off 34 balls with three fours and a six before he became Brar's first victim of the game and of his IPL career.
"My first IPL wicket is Virat and that helps. Your body opens up, you get confident, and things fall into place," said Brar.
Harshal Patel contributed a late cameo of 31 off just 13 balls but the damage had been done by then as Punjab's spinners slammed the brakes on their opponents who finished on 145-8.
Wrist spinner Ravi Bishnoi finished with 2-17 off his four overs with the impressive Brar claiming 3-19.
Brar dismissed stars Kohli, Glenn Maxwell (0) and AB de Villiers (three) without conceding a run.
"We were preparing him (Harpreet), I can say that now after a game like this," said Rahul.
"We needed a finger-spinner who could hit the hard lengths and get some spin. And we're happy it worked out."
Kohli admitted his team fell short in the chase.
"They got off to a decent start and we pulled things back decently. Probably we gave away 25 too many at the end, we should have been chasing 160," said the India skipper.