Jeje Lalpekhlua's 51st minute strike seemed like it would be enough for Chennaiyin FC to walk away with three full points. Mumbai never seemed to be into the game until Costa came off the bench to score a wonderful long ranger in the 88th minute to win their first ever point in the ISL against Chennaiyin FC.
In four previous clashes between the two teams, Chennaiyin FC had emerged triumphant in all games.
With coach Marco Materazzi suspended for this clash for his 'misconduct against opponents or persons other than match officials' in his side's previous match, the defending champions took it upon themselves to continue their dominance over the visitors.
For the opening 45 minutes, Chennaiyin FC dominated but could not break the deadlock. Maurizio Peluso was in fine form upfront and seemed to create the best chance for Jeje in the 14th minute when he slid a ball to the India striker but Gerson Vieira did well to come from behind and clear the ball.
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Mumbai City did not have any shot on target in the first session but marquee player Diego Forlan did come close in the 36th minute. The Uruguayan striker made space for himself just outside the box and let go of a powerful shot which Chennaiyin FC goalkeeper Duwayne Kerr did well to tip over for a corner.
Chennaiyin FC had their noses in front in the second session. Peluso's corner-kick should have been cleared by the Mumbai defence but two defenders simply watched and another one missed the flight of the ball, allowing Jeje space to head the ball past the goalkeeper in the 51st minute.
Mumbai City made the best use of that let-off and found the equaliser in the 88th minute. Leo Costa took the ball from about 25 yards out and launched a powerful left-footer which found the top corner of the net, past a diving Kerr.