Narine (3 for 24) and Chawla (3 for 19) snapped three wickets each as Kolkata Knight Riders produced a disciplined bowling display to test the table-toppers in their stipulated 20 overs.
Put into bat, Punjab lost Cheteshwar Pujara (8) early in the second over when Manish Pandey's direct throw from point found the opener short.
Coming into bat at number three, Wicket-keeper batsman Wriddhiman Saha (14) got a life early when a running Umesh Yadav spilled his catch but the Kolkata cricketer failed to make use of the chance.
After a four and six, he was sent back into the pavillion by experienced Jacques Kallis, who trapped him infront of wicket on his first delivery.
Glenn Maxwell then came into the crease much to the anticipation of his fans and the Australian obliged them with a reverse sweep off Sunil Narine for a boundary which also brought up the fifty for Punjab in 5.5 overs.
But then the 25-year-old decided to throw away his wicket when he went for an over-ambitious shot on the leg side only to see his leg-stump go for a walk.
David Miller then joined Sehwag but the South African's 10-ball 14-run innings, which was studded with back-to-back fours off Kallis, was cut short by leg-spinner Chawla in the 10th over.
Brought in the team in place of R Vinay Kumar, Chawla bamboozled Miller with a googly which the batsman failed to read and his slog ended up at the hands of Albie Morkel at long-on.
Skipper George Bailey then joined hands with Sehwag as the duo slammed a boundary each off Yadav in the 11th over.
The Delhi dasher then cut one at the point area off Chawla for another four.
However, Chawla came back to remove both the batsmen -- Bailey and Sehwag -- in the 14th over.