Kolkata were 7-2 in the second over before contributions of 17 from Ajinkya Rahane and 37 from Raghuvanshi appeared to settle any nerves.
Rahane became Chahal’s first victim, lbw attempting a slog sweep, to leave the score 62-3, and Raghuvanshi followed in Chahal’s next over.
“I will take the blame,” Rahane said.
“As the captain I played the wrong shot – it started from there. We batted really badly as a batting unit.
“The bowlers did really well on this surface. We were reckless – we should take full responsibility as a batting unit. It was an easy chase for us.”
Punjab looked to have little chance at halfway after their own collapse from 39-0 to 111 all out in 15.3 overs.
Openers Prabhsimran Singh and Priyansh Arya made 30 and 22 respectively as seamer Harshit Rana took 3-25.
Punjab are now fourth but join four other sides on eight points at the top of the table, while KKR are sixth.