The result meant that Chennaiyin finished second in the points table, behind Bengaluru FC, with 32 points.
A new-look Chennaiyin team, with the coach ringing in the changes, kept a determined Mumbai City team at bay, with some good defending.
A Balwant Singh goal for Mumbai in the dying seconds was disallowed, as he was off-side.
The second half saw both teams step up the attack though Chennaiyin FC looked sharper and likely to break through.
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Slovenian Rene Mihelic slotted the ball past a diving Arindam Bhattacharja to give the all-important lead, sending the home fans into raptures.
The first half was an equal battle with both teams enjoying periods of ascendency. The home team started well but Mumbai City slowly grew into the game by enjoying the greater possession.
There were a few attempts on either end, with the best one falling to Chennaiyin FC. Jude Nworuh had his shot deflected onto the post which was then eventually cleared out.
Chennaiyin's big opportunity came when Gavilan pressed forward with the ball, cut inside on his left and then fell as Lucian Goian slide to take the ball. He appealed for a penalty, but in vain.
Raju Gaikwad attempted to clear the ball, but his shot went towards Nworuh, who took a shot which went through the goalkeeper Arindam Bhattacharja's legs, but brushed the inside of his thigh on its way behind and hit the post. A Mumbai defender quickly cleared it much to the team's relief.
The prolific Jeje Lalpekhlua and in-form mid-fielder Raphael Augusto were left out, ahead of the play-offs.
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