Chasing a modest 132, the Bangalore batsmen – including Kohli, Chris Gayle and AB de Villiers – crashed in just 9.4 overs to mark a new low for the Twenty20 tournament, now in its 10th edition.
Opener Kohli's first-ball duck started the rot for Bangalore, as none of their batsmen reached double digits and Kedar Jadhav top-scored with nine at Kolkata's Eden Gardens.
It set an unwanted new IPL record after Rajasthan Royals, currently barred over a spot-fixing scandal, totalled just 58 against Bangalore in 2009.
"Our worst batting performance, it really hurts," a disappointed Kohli said on Sunday, as Bangalore stayed bottom of the eight-team IPL table.
"There's nothing to review anything about the second half, it was that bad. We need to forget it and move forward. We're a much better team," he added.
Kolkata bowler Nathan Coulter-Nile, who was man of the match for his 3-21, had Kohli caught by Manish Pandey in the very first over to trigger the rout of last year's runners-up.
England's Chris Woakes and New Zealand fast bowler Colin de Grandhomme returned figures of 3-6 and 3-4 as Bangalore lost their last six wickets for only nine runs.
"I'm sure we won't bat like that again in the tournament... We've got back-to-back games, need to try and win those to get some momentum," said Kohli.
For Kolkata, the West Indies' Sunil Narine top-scored with his 17-ball 34 while opening the innings for the home side.