The Iranian club remained at the top of its group, thanks to an early goal by Brazilian striker Shimba while Al-Gharafa was left heartbroken as the defeat left it with no chance of advancing to the next stage.
Foolad is scheduled to play Shabab Al-Ahli on Tuesday. The winner of the match will qualify for the next stage as the first team.
Already-eliminated teams Ahal and Al-Gharafa will lock horns on the same day.