Farshad Faraji put Persepolis in front in the 53rd minute but substitute Ahmed Al Ganehi levelled just three minutes later.
The visitors squandered a series of opportunities in the late minutes to take all three points.
Al Gharafa has collected four points from its first four games in the league phase while Persepolis continues to look for its first win with Juan Carlos Fernandez’s side on two points at the halfway stage.