Olunga, who left Japan's Kashiwa Reysol to join Al Duhail earlier this year, struck twice in the first half before completing his hat-trick in the 85th minute to put the Qataris on top of Group C with seven points from three matches.
Al Duhail, who were dethroned as champions by Xavi's Al Sadd in the Qatar Stars League in March, have not been a real force at the continental level, having never progressed beyond the quarter-finals.
But Wednesday's performance must have lifted their hopes with Olunga scoring his second hat-trick this year, having starred in Al Duhail's 6-0 win against Al Ahli in Qatar's Amir Cup.
Esteghlal took the lead at the King Abdulla Sports City in Jeddah with Amir Motahari powering in a header off a Seyed Mousavi cross in the fourth minute.
The 6ft 4in Olunga then took charge of the game, netting the equaliser in the 10th minute after Esteghlal goalkeeper Mohamed Mazaheri had parried a powerful shot from Edmilson onto his path.
Olunga was in the thick of the action in the 27th minute taking advantage of a wayward pass from Masoud Rigi inside the box and firing home.
Al Duhail's lead didn’t last long as Chieck Diabate scored with an easy tap-in in the 34th minute after Motahari had crossed to him following a great pass by Farshid Esmaeili.
However, just on the stroke of half-time Al Duhail were a goal up again with Abdullah al-Ahrak finding the net off a cross from Mohamed Musa.
There was more drama to come as the Iranians drew level once again with captain Esmaeili scoring in the 74th minute with a diving header following a corner.
The match appeared heading for a draw when Olunga completed his hat-trick by controlling a cross from Ismael Mohamed and firing home.
In Group A, Saudi's Al Hilal consolidated their position at the top with a 3-1 win over Tajik debutants Istiqlol at the Prince Faisal Stadium in Riyadh.
Hattan Bahebri scored a second half brace for Al Hilal, who won the title in 2019 but were thrown out of last year's competition because of a spate of coronavirus infections among the squad.
Earlier in the match, Istiqlol's Vahdat Hanonov had struck in the 41st minute to equalize after Al Hilal had gone ahead in the 39th minute through Ali al-Bulaihi.
Also in Group A, Uzbekistan's AGMK recorded their first win in the competition, beating the UAE's Shabab Al Ahli 2-1 in Riyadh.
Ahmad Hashmi had given Shabab a 29th minute lead, but goals in the dying minutes of the match by Serbian Jovan Dokic and Akramjon Komilov clinched victory for AGMK, who are also playing the tournament for the first time.
In a late night Group C match, Al Ahli of Saudi Arabia beat Iraq's Al Shorta 3-0 for their first win in three matches.
Abdulla Tarmin and Driss Fettuohi scored in the first half and Abdulrahman Ghareeb netted the third in added time as Al Ahli handed Al Shorta their third straight defeat.