Both sides had chances but failed to finish with Saudi Arabia's Al Nassr set to host Iran's Esteghlal in the return leg on March 11.
Al Nassr was missing five-time Ballon d'Or winner Cristiano Ronaldo and Aymeric Laporte, who scored the only goal when the sides met on Matchday Three of the League Stage.
Esteghlal will travel to Saudi Arabia to play Al Nassr in the second leg next week.