In the absence of Nigerian defender Bello Rasaq who was red-carded in their previous match, United's backline looked sloppy as Odafa Okolie gave Mohun Bagan a 19th minute lead.
But Sukhen Dey's strike seven minutes later turned it around for United as they settled the issue through man-of-the-match Kayne Vincent in the 42nd minute.
However, the United equaliser appeared to be an own goal by Mohun Bagan defender Khelemba Meetei in a tussle with Ranty Martins.
Even the green-and-maroon side's coach Santosh Kashyap admitted it was a "mistake" by their defender but the match commissioner R D Sow awarded the goal to Dey.
All the action was confined to the first-half of the match as Mohun Bagan failed to convert their chances to suffer their second successive defeat.
Mohun Bagan's over dependence on their top forward Odafa once again did not help their cause as they lacked cohesion, while their weak defence continued to disappoint.
Miffed with the pathetic show since the Federation Cup, the partisan 10,000-odd Mohun Bagan supporters agitated after the match crying for the coach's ouster as police had to pacify the situation.
Admitting that the forward duo of Odafa and Ozbey lacked fitness, Kashyap sought more time.
"Don't know why... But one win and everything will fall in place. Odafa and Ozbey still need to be more fit. It's a long tournament and I am sure we will back to winning ways," Kashyap told reporters after the match.
United coach Sanjoy Sen was all excited after their back-to-back wins and said they were the title favourites this time around.
"The win is bigger than the one against Air India. We consider ourselves for the title now. We have to keep winning against the big teams like Mohun Bagan, Churchill and Dempo," Sen said.
He said their team did not look back after getting the equaliser.
Having missed a one-on-one against Subrata Pal in the 16th minute, Odafa was at it again as he brilliantly tackled the United custodian minutes later for the lead.
But Mohun Bagan defence could not hold on when United began a move through Dey resulting in a goal that seemed to have taken the deflection of Meetei.
Vincent also missed a chance in the 31st minute but he soon made amends by scoring the match-winning goal from a Carlos Hernandez centre before the break.
Mohun Bagan had the better possession after the change over but it was not enough as the Odafa and Ozbey duo lacked the sting.
After two rounds, United now have six points while Mohun Bagan are yet to open their account.
