Dinesh Kumar (66kg), Ajit Singh (84kg) and Surjeet (120kg), who won their opening bouts with relative ease, all lost to Azerbaijan opponents in the next contest of their respective weight categories to crash out of the competition.
Devender Kumar, however, made it to the third round of the 55kg category before going down to Armenia's Artak Hovhannisyan in a closely fought duel at Arena Armeetz.
India finished at the 11th position in the freestyle team rankings with 14 points, which were dominated by Russian wrestlers (64) followed by Iran (52).