Vafa Hakhamaneshi scored the only goal of the game in the 69th minute, not long before he was sent off.
Both sides ended with ten men as East Bengal Sarthak Golui was also sent off in the 75th minute.
The hosts were unchanged as head coach Stephen Constantine played the same XI that started last week in the Kolkata Derby.
Chennaiyin FC made only one substitution, with Debjit Majumder returning in goal after serving his suspension. The biggest concern for the visitors was the absence of Kwame Karikari from the squad due to an injury.
Two minutes into the game, Jordan O’Doherty found himself in space in the Chennaiyin box. His pass was blocked by Fallou Diagne before it could do any damage.
On the other hand, just after 10 minutes, Petar Sliskovic was knocked out by Anirudh Thapa with a through ball. The corner was tight and Sliskovic’s effort hit the post.
Halfway through the first half, Suhair Vadakkepeedika tried to overwhelm the visitors with a quick counterattack. The flag hung as Suhair galloped toward the goal before setting his effort wide of the far post.
In the 34th minute, Thapa sold a dummy into the East Bengal box before seeing his powerful shot saved by Kamaljit Singh.
In the 36th minute, Hakhamaneshi was almost punished for his complacency on the edge of the Chennaiyin box. The Iranian delayed a pass to the goalkeeper before losing his balance. Cleiton Silva jumped the ball, but saw his shot miss the goal from a tight angle.
Five minutes into the second half, a corner from Chennaiyin FC was cleared, but only to Rahim Ali, who was lurking on the edge of the penalty area. On the volley, the striker tried to find the bottom right corner, but his effort went just wide.
Three minutes later, Kamaljit produced another brave save to deny Prasanth Karuthadathkuni.
The match was 0-0 until the 69th minute.
Substitute Akash Sangwan tapped in a good ball from a corner and Hakhamaneshi was the first to reach it and nodded in from close range, giving the Marina Machans a crucial lead.
However, the Iranian defender received a second yellow card of the match because of his party and the number of visitors was only 10 men.
Just over five minutes after the incident, the Torch Bearers had also been reduced to ten men. Sarthak, who was booked in the first half, got his marching orders after connecting his elbow with Anirudh Thapa in midfield.
The three points move Chennaiyin FC from sixth to fifth in the ISL table.
With seven points, the Marina Machans are three points behind and will play at home against Mumbai City FC on November 12.
East Bengal dropped from ninth to tenth place in the league. The Torch Bearers are three points behind and will face Bengaluru FC on November 11.