Al-Nassr's win in Riyadh on Monday came after a 0-0 draw in the first leg in Tehran last week and takes Stefano Pioli's team into the quarter-finals, which will be played in Jeddah as part of a centralised tournament from April 25 to May 3.
Former Aston Villa striker Duran put Al-Nassr in front after nine minutes and the Saudis doubled their lead from the penalty spot, Cristiano Ronaldo stepping up in the 27th minute to convert with typical confidence following Mohammad Niknafs' mistimed challenge on Sadio Mane.
Esteghlal's task was made almost impossible when Mehran Ahmadi was sent off for a second bookable offence late in the first half as he caught Mohammed Al-Fatil in the face with a flailing arm.
Colombian Duran claimed his second goal of the game six minutes from time when he whipped a low strike into the bottom corner having earlier hit the post as Al-Nassr eased through.
"I think we played well," said ex-Liverpool winger Mane.
"We created many chances and we scored three goals. I think we got our reward.
"We pressed well together, we pushed them and they made mistakes and from that we scored three goals. We have a clean sheet and we cannot expect more than this."
Elsewhere, Al-Sadd beat Al-Wasl 3-1 in Doha for a 4-2 aggregate win over the side from the UAE.
Al-Sadd progressed as a result of an 11-minute spell in the first half that saw the Qataris score three times to overturn Fabio Lima's early opener.
Asian Player of the Year Akram Afif unlocked the Al-Wasl defence to haul Al-Sadd level 16 minutes later.
Youcef Atal's strike saw Al-Sadd take the lead on the half-hour and Afif showed his quality with the third in the 37th minute, playing a short free kick to Claudinho and then bending the return into the top corner from 20 metres.
