Chennai will now play the Second Qualifying Match against Delhi Daredevils on Friday at their home ground.
Chasing 188 to win, Mumbai openers Sachin Tendulkar and Dwayne Smith provided a good start of 47 but as soon Tendulkar was run out for 11, his team begin to collapse and lost wickets at regular intervals as they could reach 149 for nine in the allotted 20 overs.
Smith top scored with 38 in 22 balls with two sixes and five fours.
For Chennai, pace bowlers Dwayne Bravo of West Indies and Albie Morkel of South Africa claimed two wickets each for 10 and 31, respectively.
Earlier, Mumbai captain Harbhajan Singh won the toss and put Chennai into bat who made 187 runs for five wickets in 20 overs.
Captain Mahindra Singh Dhoni made an unbeaten 51 off 20 balls with six fours and two sixes. Among other prominent scorers were Michael Hussey scored 49, Subramaniam Badrinath 47 and Bravo remained not out on 33.
Medium-pacer Dhawal Kulkarni captured three wickets for Mumbai
