The Super Kings, who had made three changes from the team that had beaten Rajasthan Royals last week, bowled and fielded with intensity to emerge deserving winners.
For the home team, left-arm seamer Thilan Thushara (2 for 16) and off-spinner Ravichandran Ashwin (2 for 22), both coming in as a replacement for Tuesday's game, were outstanding, though the former had to be taken off midway through his third over after being no-balled twice.
However, the hosts had to work for their runs after deciding to bat first on winning the toss as they huffed and puffed their way to 165 for four in 20 overs against a highly efficient Mumbai Indians.
For Mumbai, off-spinner Harbhajan Singh was the pick of the bowlers with a two-wicket haul, but it was seamer Kieron Pollard whose two wickets in one over applied brakes on the Super Kings.
None of the Super Kings batsmen, including Murali Vijay, a centurion in the previous game here, was able to raise a gallop by T20 standards with the Mumbai bowlers keeping it tight, backed by precise field placements.
Opener Matthew Hayden top scored with 35, but was never able to dominate while the rest got good starts only to depart at regular intervals.In Image: R Ashwin of the Chennai Super Kings is congratulated by Mahendra Singh Dhoni , after bowling Ryan McLaren of the Mumbai IndiansScores | Coverage: IPL 2010