Chasing 157, Chennai could manage 149 runs for the loss of eight wickets in 20 overs.
Dwayne Bravo of the West Indies made 30, Faf du Plessis of South Africa scored 29 and Subramaniam Badrinath hit 25 as only two other batsmen could get into double figures.
Pakistan-born English county all-rounder Azhar Mahmood captured three wickets for 25 runs and India’s leg-break bowler Piyush Chawla claimed two for 20 for Punjab.
Earlier, Kings XI Punjab made 156 for eight in the allotted 20 overs after their captain David Hussey won the toss.
Mandeep Singh top scored with 56, followed by Shaun Marsh of Australia who made 32. Both openers provided a good start of 68 but later no other batsman could get into double figures except South Africa’s David Miller (19) and Azhar Mahmood (18).
For Chennai, Albie Morkel of South Africa got three wickets for 29 and Bravo took two for 28.
Pakistan’s premier sports tv channel Geo Super televised this interesting match live from Chennai