Their blockbuster batting line-up, containing the likes of prolific India captain Virat Kohli, swashbuckling West Indian Chris Gayle and the versatile South African AB de Villiers, were bundled out for 49 inside 10 overs.
Skipper Kohli fell for a first ball duck, Gayle made seven and de Villiers managed eight with none of the Bangalore batsmen reaching double digit after restricting Kolkata to 131.
"Our worst batting performance," Kohli said after the team's spectacular meltdown at Eden Gardens. "It really hurts. After the kind of half that we had, we thought we could capitalise and chase it down.
"Reckless batting, I can't say anything at the moment. It was that bad. This is just not acceptable."
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Rajasthan Royals' 58 against Bangalore in 2009 was the previous lowest total.
With their fifth defeat in seven matches, last year's runners-up Bangalore slipped to the bottom of the points table at the halfway stage of the Twenty20 tournament.
"We need to forget it and move forward. We're a much better team," said Kohli, who missed Bangalore's first three matches with a shoulder injury.
"We got 200 plus in the last game. I'm sure everyone realises what they've done wrong. You have to come out, show intent and back yourselves. I'm sure we won't bat like that again in the tournament."
Kolkata's pace attack claimed all 10 Bangalore wickets with Australian Nathan Coulter-Nile, England's Chris Woakes and New Zealander Colin de Grandhomme claiming three each.
Woakes said the track at Eden Gardens was fair to the seam bowlers.
"It definitely assisted the seamers and it is probably the first time that we had good pace and carry since the time we started playing here," said the 28-year-old all-rounder.
"It swung a bit to start with as well which helps. But you still got to put the ball in the right areas and we managed to do that tonight."
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
