Thereafter, Bravo and Morkel added 36 runs for the seventh wicket before the West Indian all-rounder was caught in the deep in the 19th over. At that stage, the Super Kings needed 21 off eight deliveries.
Morkel departed in the last over bowled by Mahmood, holing out in the deep. New man Ravichandran Ashwin reverse hit a boundary, but a single off the next effectively ended the Super Kings' challenge as they needed 11 off two, a target that proved beyond them.
Earlier, Marsh's freak run out while backing up undid all the good work that the Aussie opener had done in the company of Mandeep Singh as the pair had put on 68 runs in eight overs.
Mandeep's hard drive down the pitch struck Ashwin on the foot and deflected on to the stumps with Marsh caught outside the crease to be run out.
Image: Kings XI Punjab's Mandeep Singh plays a shot during their Indian Premier League (IPL) cricket match against Chennai Super Kings, in Chennai, India, Sunday, April 28, 2012.