Striker CK Vineeth opened scoring for the visitors in the 16th minute before Mumbai FC new-signing Sandjar Ahmadi (20th min) equalised for the hosts four minutes later.
With one point from today's match, Mumbai FC stay in the fourth place, still unbeaten with six points from four games while United SC are at third in the table with seven points from four games.
The game burst into action inside two minutes when Vineeth did well to set up strike partner Ranti Martins. The Nigerian ran clear of his marker, defender Anwar Ali, to create space but his shot rebounded from the upright.
Vineeth held off challenges from two defenders before slotting home past keeper Kunal Sawant.
The hosts equalised almost instantly with Ahmadi opening his account for Mumbai FC. Striker Orok Essien did well to get a shot from the left straight towards United SC custodian Sangram Mukherjee who managed to block. However, the rebound fell for Ahmadi, who cleverly timed his run to slot the ball into the net.