The match ended 1-1 after first-half goals from Roy Krishna and Jay Gupta.
Odisha won 3-0 with Roy Krishna also scoring in the away match.
The Blasters had led through Dimitrios Diamantakos goal in the first half.
Roy Krishna scored a brace as Odisha scored all four goals in the first half.
Odisha rode on an early opener by Fijian forward Roy Krishna as the home side fell short of building upon their maiden victory they notched last week against Chennaiyin FC.
East Bengal have kept four clean sheets in a row in the ISL.
Odisha won 3-0 with Mourtada Fall also joing the scoresheet.
The hosts held Odisha 2-2 at the Salt Lake Stadium in Kolkata.
The Fijian met the corner kick by Ahmed Jahouh with utmost precision and slotted it into the net from close range.
Brazilian striker Diego Maurcio scored the winner.