Glenn Maxwell (44; 25b; 1x4, 4x6) and Wriddhiman Saha 38 (33b; 2x4, 1x6) stitched together a 71-run stand for the fourth wicket but it was KKR's England all-rounder Chris Woakes who stole the show with best bowling figures of 2/20 in his alloted four overs.
Left-arm wrist spinner Kuldeep Yadav also returned decent figures of 2/34 as the Gautam Gambhir-led side never let the Punjab batsmen pull away.
Axar Patel (not out 8) and Rahul Tewatia (not out 14) were at the crease at the end of the innings.
In the absence of Hashim Amla, Martin Guptill opened the batting with Manan Vohra. The pair did not last long though. First to go was Vohra (25; 16b; 4x4, 0x6), falling to in-form fast bowler Umesh Yadav trying to play fine down the leg side with the ball kissing the glove and carrying to fit-again wicket-keeper Robin Uthappa.
In the next over, Narine got Guptill (12; 16b 1x4 0x6) leg before wicket. After Powerplay overs (6), the hosts were 41/2.
Shaun Marsh looked good for his 11, milking two boundaries before Chris Woakes castled him.
Maxwell and Saha stemmed the rot with a cautious association. Punjab were 63/3 at the halfway stage. Just when Maxwell tried to up the ante, tonking Kuldeep Yadav for two consecutive sixes only to get out in the next ball. Trying to clear the fence again, the big-hitting Australian forced Woakes to run across from long-off and complete a superb catch.
Swapnil Singh departed soon after adding just two runs to the total as the visitors reined in the run flow in the final overs.
Brief scores: Punjab: 166/6 in 20 overs (Glenn Maxwell 44, Wriddhiman Saha 38; Chris Woakes 2/20, Kuldeep Yadav 2/34) vs Kolkata.