The Iranian team suffered an early blow as forward Mehdi Torabi had to be stretched off inside the opening 10 minutes following an injury, being replaced by Shahab Zahedi.
Persepolis midfielder Milad Sarlak received his second yellow card following a late challenge on Cristiano Ronaldo in the 51st minute.
Abdulrahman Ghareeb scored the opener for Al Nassr in the 62nd minute and Mohammed Qassem made it 2-0 in the 72nd minute.
Al Nassr will welcome Istiklol to the King Saud University Stadium in Riyadh, while Persepolis will travel to Doha to face Al Duhail who had drawn 0-0 with Istiklol earlier on Tuesday.