Both teams were vying for their first win, having suffered defeats against Australia (0-2) and the Philippines (1-4) respectively.
Iran almost shocked Chinese Taipei in the fourth minute of added time when Samaneh Chahkandi slipped a shot through an onrushing Chinese Taipei keeper Cheng Ssu-yu, only for Ting Chia-ying to scramble the ball to safety.
Iran will meet the Philippines on Wednesday, while Chinese Taipei play Australia.