Forward Abdullrazak Al Hussain scored both the goals for the Iraqi outfit.
Al Hussain put the hosts in lead by scoring in the first half's added time and found another immediately after the change of hands, in the 47th minute at the Franso Hariri Stadium.
East Bengal's chances of progressing to the next round had already suffered a jolt after they lost by a similar margin in the first leg in Kolkata last week.
Today's defeat was East Bengal's fourth successive in the tournament having beaten 0-1 by Al Orouba of Yemen and 0-3 by Kazma of Kuwait in their earlier two group matches, besides the last one against Arbil. PTI AH