Besides man-of-the-match Talgat's four goals in 23rd, 82nd, 84th and 90+3 minutes, Chruchill Brothers scored through Ansumana Kromah (67th) and Brandon Fernandes (90th).
Chennai City, who were reduced to 10 players in the second half, netted the ball through Michael Soosai Raj in the 54th minute.
This win takes Churchill Brothers to 20 points from 17 matches. They will play their last match against Bengaluru on April 29.
They would be finishing sixth even if they lose to Bengaluru.
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Mumbai City, who are lying at the bottom, would be relegated as they would finish behind Churchill Brothers at the end of the league.
Churchill Brothers, needing a win to avoid relegation, played with their beat team.
Both the teams made a slow start, trying to gauge each other's strength but Churchill Brothers controlled the proceeding and managed to make inroads.
The visitors came up with occasional forays and had their best chance in the 37th minute but Edwin Sydney's effort missed the target narrowly.
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