Chasing 165 for victory, Chennai Super Kings were restricted to 156 for nine.
Harbhajan was the pick of the bowlers, taking five for 18 in his four overs.
S. Badrinath remained unbeaten on 71 while Michael Hussey contributed 41.
Mumbai Indians:
Rajagopal Sathish c Anirudha b Morkel 0
Sachin Tendulkar c Hussey b Bollinger 5
Ambati Rayudu st Dhoni b Randiv 27
Rohit Sharma c Hussey b Bollinger 87
Andrew Symonds not out 31
Kieron Pollard not out 0
Extras (b 1, lb 1, w 12) 14
Total (for four wickets in 20 overs) 164
Fall of wickets: 1-9 (Sathish, 2.1 overs), 2-13 (Tendulkar, 3.4), 3-74 (Rayudu, 11.1), 4-161 (Sharma, 19.2)
Bowling:
Albie Morkel 4-1-19-1
Doug Bollinger 4-0-30-2
Joginder Sharma 3-0-34-0
Ravichandran Ashwin 4-0-26-0
Suraj Randiv 3-0-31-1
Suresh Raina 2-0-22-0
Chennai Super Kings:
Michael Hussey c Pollard b Malinga 41
Murali Vijay c Sharma b Patel 12
Suresh Raina c & b Harbhajan Singh 5
Subramaniam Badrinath not out 55
Mahendra Singh Dhoni c Sharma b Pollard 3
Srikkanth Anirudha c Sathish b Harbhajan Singh 9
Albie Morkel b Harbhajan Singh 3
Ravichandran Ashwin c Pollard b Harbhajan Singh 0
Joginder Sharma c & b Harbhajan Singh 0
Suraj Randiv c Sathish b Malinga 2
Doug Bollinger not out 0
Extras (lb 1, w 8, nb 1) 10
Total (for nine wickets in 20 overs) 156
Fall of wickets: 1-31 (Vijay, 3.4 overs), 2-38 (Raina, 4.5), 3-98 (Hussey, 11.2), 4-101 (Dhoni, 12.2), 5-123 (Anirudha, 15.6), 6-136 (Morkel, 17.2), 7-136 (Ashwin, 17.4), 8-137 (Joginder Sharma, 17.6), 9-140 (Randiv, 18.5)
Bowling:
Munaf Patel 4-0-40-1
Lasith Malinga 4-0-20-2
Abu Nechim Ahmed 2-0-19-0
Harbhajan Singh 4-0-18-5
Rohit Sharma 1-0-15-0
Kieron Pollard 4-0-30-1
Rajagopal Sathish 1-0-13-0
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