Defederico and Krisztian Vadocz scored the goals for the hosts which was them through for the next round. Mumbai have bagged 22 points playing 13 matches.
Chennaiyin FC, on the other hand, struggle at the 7th position with only 14 points from 12 matches. The last two matches are now virtually do or die for Marco Materazzi's men.
This will Mumbai City FC's maiden appearance in the play-off stage. Their last match will be against Delhi Dynamos on December 3.
Here are some pictures from the match
Chennaiyin FC co-owner Abhishek Bachchan watching the match from the stands.
Mumbai City players
Mumbai City FC players celebrate after scoring a goal.
Diego Forlan and Defederico
Mumbai City FC captain Diego Forlan celebrates with teammate and goal scorerDefederico.
Sunil Chhetri (right)
Fans' Player of the Match Sunil Chhetri tussle for the ball with a Chennaiyin FC player.
Krisztian Vadocz celebrates after scoring the second goal for Mumbai City FC,
All photos are taken from Indian Super League official Twitter handle