Nosrati opened the account for Amir Ghalenoieeâ€™s team on 20 minutes before Nekounam added to it six minutes into the restart.
The win, coming after Iranâ€™s 1-1 last-gasp draw against Korea Republic, took Team Melli to eight points in Group B, two points behind current leaders Korea Republic, who earlier thrashed Chinese Taipei 8-0.
This was also coach Ghalenoieeâ€™s first victory in a competitive match.
Iran, who have qualified for every Asian Cup since 1968, started brightly in the qualifiers with a 4-0 trouncing of Chinese Taipei before being held 1-1 by Syria. Only a last minute goal by Vahid Hashemian helped Team Melli eke out a 1-1 draw against the Koreans in the previous round.
Iran will be looking to build up on this win against Chinese Taipei at Taipei on October 11 while the Syrians will be aiming to bring their campaign back on track against Korea Republic in Seoul.