Joel Kojo gave the Iranians the lead in the fourth minute but Rewan Amin leveled four minutes after the interval for the visitors, whose slim chances of a top eight finish in the league phase and a last 16 berth now hinge on results in other matches.
The draw moves Esteghlal onto six points from seven matches with Al Shorta on three, meaning defending champion Al Ain cannot climb into the qualification places for the knockout rounds with one league phase match remaining.
Esteghlal will meet Al Rayyan on Matchday 8 on February 18 in Doha, Qatar.