The late drama sparked wild celebrations from the Iran bench in St Petersburg as Carlos Queiroz's side took three points from a game in which they were second best for long periods.
Herve Renard's well-organised team extended Morocco's record of never having won their opening game in the tournament despite dominating the match and carving out opportunities to score either side of half-time.
Iran's counter-attacking strategy had failed to bear fruit with Karim Ansarifard and Sardar Azmoun squandering great chances until their wastefulness was rendered irrelevant by Bouhaddouz's late error.
The Morocco striker, on as a substitute in the 77th minute, put Ehsan Haji Safi's free-kick through his own net with a diving header in the 95th minute of the game, leaving no time for a comeback.
While Iran celebrated, Morocco faced up to the daunting reality of going into their remaining Group B games against Spain and Portugal with no points on the board.
