Both have struggled to get going domestically and will have to find their best form if they are to hit the ground running at the Shahr-e Qods Stadium near Tehran.
Esteghlal will hope to make home ground advantage count, with the two meeting for the first time since they clashed in the group stage of the AFC Champions League 2010.
Esteghal won the home tie then 3-0 but the Iran side has only triumphed once in its last seven opening matches on the continental stage.
Al Gharafa was held 1-1 by Al Shamal in the Qatar Stars League tie on Friday, the result taking the team to five points from four matches.
They will, however, draw on the high of having defeated UAE side Shabab Al Ahli in the preliminary stage to get a result against the Iranian opponent.