It was fourth win for Kings XI who remain in seventh spot with eight points while the Super Kings, who are third, suffered their fourth defeat in nine outings and are on nine.
The Super Kings were off to a flier as openers Francois du Plessis (29 off 20 balls) and Subramaniam Badrinath (25 off 18) put on 56 runs by the fifth over, but the introduction of Mahmood turned the game on its head as he removed the pair.
Both du Plessis and Badrinath were deceived by slower deliveries in consecutive overs and thereafter, the Super Kings lost three more wickets in quick time with Suresh Raina (15), Wriddhiman Saha (7) and skipper Mahendra Singh Dhoni (1) departing as the hosts slid to 88 for five in the 14th over.
More drama was to follow in the next over bowled by Chawla as Dwayne Bravo (1) was dropped by Shaun Marsh, but two balls later, Ravindra Jadeja (17) was caught by David Hussey after mistiming a big hit.
Image: Kings XI Punjab's David Hussey collides with Chennai Super Kings' Dwayne Bravo while running between the wickets during the Indian Premier League (IPL) cricket match, in Chennai, India, Sunday, April 28, 2012.