After a barren first half, Bagan scored through Nikhil Kadam (54th minute) and Akram Moghrabi (76th). Churchill Brothers pulled one back through Osagie Moday in the 74th minute in the match played at Tilak Maidan.
Mohun Bagan now move to third place with 30 points and play their last match against Gokulam Kerala on March 6 in Kozhikode.
Churchill Brothers, meanwhile, remained on ninth place with 17 points. They play Minerva Punjab on March 8 in Panchkula in their last match.
Churchill made one change from their drawn match against Gokulam Kerala, bringing in Britto PM in place of injured Wayne Vaz.
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Both the side's played a cautious game initially which saw play confined to midfield for most part of the first half. Mohun Bagan tried to make inroads into the Churchill goal but their moves fizzled out as they found defender Monday a tough nut to crack.
Churchill had two clear chances but Jeancy Zunapio Siyo was guilty on both the occasions. First, he first headed over the bar off a cross from Britto and in the dying minute of the first half, he directed the ball wide off the mark off a Frincis pass.
Mohun Bagan broke the deadlock after the break in the 54th minute. Aser Pierrick Dipanda Dicka, who missed a clear chance after the break, played a square pass to Nikhil Kadam who unleashed a left-footer that found the far corner of the net.
The visiting side preferred to defend their citadel after taking the lead while Churchill went all out to find the equaliser.
The move paid off as Churchill found the equaliser in the 74th when substitute Nicholas Fernandes sent a measured cross into the box for unmarked Monday who tapped in.
However, Churchill's joy was short lived as Mohun Bagan once again took the lead two minutes later. Substitute S K Faiaz sent a high cross into the box for Akram Moghrabi to find the target to give Mohun Bagan full points and keep themselves in the hunt for the title.
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