Opener Kohli had reached 20 when Rabada bowled a back of a length ball into his hips. Kohli was late on a pull and the ball ballooned off his body to short fine leg.
The Proteas fast bowler went on to finish with figures of 3-21 in his four overs.
The Kings were put in to bat at the Brabourne Stadium in Mumbai and amassed 209-9 in 20 overs after Englishmen Jonny Bairstow and Liam Livingstone scored brisk fifties.
Bairstow smashed a 21-ball 66 (four fours and seven sixes) before Livingstone took charge and hit a 42-ball 70 (five fours and four sixes).
Harshal Patel (4-34) was the top wicket-taker for Bangalore.
In reply, Kohli and skipper Faf du Plessis (10) got Bangalore off to a decent start, but both fell in quick succession.
Rajat Patidar lost his wicket for 26 with Glenn Maxwell trying to accelerate the run-scoring. He hit three fours and a six in his 35 before being caught at long-off by Arshdeep Singh off Harpreet Brar.
Bangalore’s tail-enders buckled under the pressure, losing four wickets for 38 runs.
© Agence France-Presse
