Zahedi, who joined the J-League side from Persepolis in the January transfer window, was on target in the 28th minute in the match against Urawa Reds at the Saitama Stadium.
Ryoma Watanabe leveled the score in the 65th minute and Thiago Santos Santana scored the winner for Urawa from the penalty spot in the 73rd minute.
Fukuoka remained 16th in the 20-team table with five points out of five matches.
Urawa Reds sits eighth with eight points, five points behind Machida Zelvia.