Yakubu Yusif's penalty had given Mumbai FC a deserving lead in the 34th minute but Sporting hit back in the second session with goals from Dawson Fernandes (53rd minute) and Victorino Fernandes (75th minute) until Coutinho struck the equaliser in the second minute of added time.
The draw takes Sporting Clube de Goa tally to 35 points from 26 matches to remain at sixth place while Mumbai FC took their tally to 32 points to finish 8th.
Mumbai FC coach Khalid Jamil fielded a relatively unknown side, playing five players who were not part of the previous squads.
That decision seemed to have done the team some good as they controlled the proceeding and took the lead in the 34th minute when Rohit Mirza won a penalty after rival midfielder Ogba Kalu brought him down inside the box.
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Yusif Yakubu, who took the penalty, converted it to have the visitors leading 1-0 at half time.
Sporting Clube, who looked subdued and failed to threaten the rival citadel, had one chance in the first half when Dawson Fernandes' snap shot missed the target.
A long ball from Joseph Clement saw Dawson beat the offside trap and finish past goalkeeper K Sharath in the 53rd minute.
In the 75th minute, Dawson sent a defence-splitting pass that substitute striker Victorino Fernandes did well to control, beat his marker for pace and finish with ease.
It seemed as if Sporting were headed for a win but Coutinho's goal in the second minute of added time helped the visitors earn a valuable point.