After opting to bat first MI openers Lendl Simmons and Parthiv Patel were watchful to start with, but Simmons hit a few lusty blows and the duo combined for a 90-run stand for the opening wicket.
Dwayne Bravo broke the partnership removing Parthiv Patel for 35 courtesy a slower one in the 11th over.
Simmons scored his third IPL 2015 fifty off 38 balls but departed to Ravindra Jadeja for 65 off 51 balls. Simmons wicket led to a mini-collapse as MI lost three wickets for 36 runs.
Jadeja had a good day in the field claiming three catches to go along with his wicket of Simmons.
CSK managed to stifle MI in the middle overs before Kieron Pollard's 17-ball 41 helped MI post 187 for 6.
In chase of 188, CSK were off to a bad start losing Dwayne Smith to Laisth Malinga owing to a horrible decision by the umpire in the first over, followed by the wicket of Michael Hussey for 16 in the sixth over.
Faf Du Plessis (45) and Suresh Raina (25) steadied the CSK innings with a 40-run stand for the third wicket.
Harbhajan Singh then tilted the game in his team's favour by scalping Raina and MS Dhoni off successive deliveries.
CSK lost way in the chase losing wickets in heap. Jagadeesha Suchith claimed the wicket of well-set Faf du Plessis.
Mumbai Indians bowlers made short work of the CSK's lower-order and registered a 25-run win to book a place in the finals of the 2015 Indian Premier League.