Javier Siverio equalised on 45 minutes after Chennaiyin had lead through Sajid Dhot's 13th minute opener.
The winner arrived in the 82nd minute and halted Chennaiyin's entry into the top-four.
Udanta Singh and Pratik Chaudhari came off the bench to score in a 4-2 win for Bengaluru.
Ivan Vukomanovic's Kerala crushed Chennaiyin FC 3-0 on Wednesday.
Blasters had crushed Mumbai City 3-0 in their last match.
Odisha suffered their second straight defeat and dropped a rung to fifth place with nine points from six matches.
Mumbai City has 15 points from six matches and remain top of the table.
Chennaiyin are yet to taste defeat as they go third on the table with eight points.
Chennaiyin moved to the top spot with seven points from three games while East Bengal were placed ninth with two points after four matches.
Chennaiyin captain Anirudh Thapa (74th) sealed the deal with a fine strike.