After a goalless first half, Mendoza came up with two goals in the 60th and 66th minute to hand Chennaiyin FC their second victory on the trot and leave Mumbai City FC without a win in three matches.
Mendoza is now the leading goal-scorer in the league with five goals.
In what was essentially a tight game at the start, Mumbai City FC did well to cover their defence and allow limited space for Mendoza to operate.
His first chance came early in the game but the attempt was acrobatically saved by Mumbai goalkeeper Subrata Paul. His best chance, though, came in the 28th minute when Elano played a through ball but Mendoza's first touch was disappointing and he ballooned the ball over with only the goalkeeper to beat.
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In-between, there were chances for Thoi Singh, who made a mess of a beautiful through ball from Elano, while Raphael Augusto saw his grounder being saved just in time by Subrata Paul.
There was a chance for Frederic Piquionne as well after L Fanai freed himself on the left flank and marched ahead but his cross right inside the rival goalmouth was wasted by the French striker.
Chennaiyin FC broke the deadlock at the hour mark after Mumbai City FC erred. A costly mistake from defensive midfielder Prathesh Shirodkar just outside the box allowed Elano to latch on to the ball and then easily lay it for Mendoza to slam into an empty goal.