Dhanachandra Singh fired his side to lead from a Katsumi Yusa corner kick in the 27th minute and Balwant Singh headed home the second in the 85th minute from a Yusa freekick at the Viveakananda Yuva Bharati Krirangan.
Moments after conceding the second, both teams were reduced to 10 players as Dempo's star forward Carlos Hernandez and Mohun Bagan's midfielder Shehnaz Singh were sent off following an unsavoury scuffle.
But before the stadium broke into a battlefield the match officials and pacified both the parties and sent off the duo.
Mohun Bagan (18 points) held on to the 2-0 lead and jumped past overnight leader Bengaluru FC (17) to go on top with two matches in hand against the defending champions.
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Having dished out a disjointed first half, the Goan heavyweights under new coach Trevor Morgan were quick to regroup as they looked promising after the changeover and pressed hard while Mohun Bagan played a catching up game.
"We badly wanted to win. All of us gave 100 percent and the three points will give us confidence in due course. I just followed my coach's advice," Majumder said as they shift their focus on the high profile derby against East Bengal on March 28.
After eight matches, Mohun Bagan also remain the only unbeaten team in the 11-team standings and coach Sanjoy Sen said, "I'm really proud of the boys. It was getting very difficult to keep the rhythm after the break but the boys showed great character."
Hernandez also had a fine opportunity in the 54th minute after being set up by Alwyn George but the Costa Rican smacked the ball over the bar.