Air India were reduced to 10 players after John Dias was sent off in the 11th minute but that did not help Mohun Bagan as the former, despite the handicap, scored through Elijah Junior (28th) and Henry Ezeh (85th) to earn full points from the group B match at Kanchenjunga Stadium in Siliguri.
Dias apparently reacted violently to a decision by referee Vishnu Chauhan.
But the Mumbai-based side showed resilience and reorganised itself well against a full-strength Mohun Bagan to find the lead in the 28th minute.
Air India striker Elijah Junior was favoured by luck as his shot rebounded into the net.
Mohun Bagan's efforts to find the equaliser went in vain as Air India bolstered their defence.
Air India goalkeeper Sukhwinder Singh also did a brilliant job saving at least three attempts from Okolie Odafa (30th), Jewel Raja (33rd) and C S Sabeeth (72nd) who was playing for an injured Tolgay Ozbey.
The result ended Mohun Bagan's hopes with one group league match left as the team tallied just one point from two matches to be at the bottom of the table.
The Kolkata ginats had earlier played out a goalless draw against Churchill Brothers in their opening fixture.
Churchill (four points) remained on top with Mohammedan Sporting and Air India behind on three.
Defending champions Salgaocar notched their second successive win, beating United Sikkim 3-0 to brighten their semi-final chances.
In other matches of the day, Churchill Brothers put their campaign on track with a 5-1 thrashing of Mohammedan Sporting, while Pune FC held United SC 1-1.
Salgaocar, who had defeated United SC in their opening tie, were once again in their elements as they scored through Philippines recruit Angel Guirado (2nd), Nicolao Colaco (81st), Anthony D'Souza (85th) at the Keenan Stadium in Jamshedpur to lead group D with six points.
A point against Pune FC would be enough for the Karim Bencherifa-coached side to secure a last-four berth.
In another match of the same group, simultaneously played at the JRD Sports Complex, United SC struck through their star Costa Rican striker Carlos Hernanandez who headed one in from a corner kick in the 14th minute.
But the Kolkata outfit could not hold the lead as Pune FC Izumi Arata brilliantly equalised through a cross header in the 62nd minute.
Pune FC (4) are now two points shy of Salgaocar in the group table, while United SC (1) and United Sikkim (zero) are out of the race.
It was a glut of goals at the Kanchenjunga Stadium in Siliguri where Goan heavyweights Churchill Brothers registered their first win with a 5-1 rout of Mohammadan Sporting.
Churchill's Lebanese recruit Bilal Nijjarin started the goal race, firing one in the 13th minute, while Bineesh Balan doubled the lead in the 29th minute.
It was their Brazilian star midfielder Beto's turn to get into the act as he made it 3-0 with a 33rd minute effort.
There was a momentary joy for Mohammadan Sporting who scored their solitary goal through Theodore Sunday in the 38th minute.
But the Goans were simply unstoppable as another Lebanese recruit Akram Moghrabi (40th) made it 4-1 at half-time.
Henry Antchouet completed the rout with an 88th minute strike.
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