Majidi (pictured) scored in either half to wrap up the three points before substitute Hassan Al Raheb grabbed a late consolation for the home side as last year's AFC Champions League winning coach Sergio Farias suffered a defeat on his continental debut in charge of Al Ahli.
With Al Gharafa recording a 2-1 win over Al Jazira in Abu Dhabi, Esteghlal share top spot with the Qatar League leaders after the opening game in Group A.
The home side began brightly, but the visitors opened the scoring after just 12 minutes as Majidi found himself on the end of a corner and dispatched his header past Al Ahli goalkeeper Abdullah Al Muaiouf.
Six minutes later midfielder Motaz Al Mosa almost equalised for the home side but a lack of fortune and a brilliant double save from Esteghlal goalkeeper Mohammad Mohammadi preserved the visitors' lead.
Striker Malek Maaz saw his initial close range effort blocked by Mohammadi before the Esteghlal custodian recovered to turn away Al Mosa's follow up header.
Former Pohang Steelers coach Farias made his first substitution after 20 minutes by replacing defender Mansour Al Harbi with Abdul Rahim Jizawi.
And the move almost paid off as Jizawi linked up with striker Victor Simoes but agonisingly guided his header from the Brazilian's cross the wrong side of the post.
The home side continued to press after the break but again Esteghlal goalkeeper Mohammadi contained to prevail.
The Esteghlal custodian did hand the home side a chance to equalise after bringing down substitute Jizawi inside the penally area, but Mohammadi made amends by saving Marcinho’s 68th minute spot kick.
And with 14 minutes remaining an unmarked Majidi doubled Esteghlal's lead as the striker headed home past Al Muaiouf.
Al Ahli attempted to press forward in the last 10 minutes in search of a way back into the contest through Al Raheb and Jizawi, but the Esteghlal defence and Mohammadi stood firm.
Mohammadi was beaten with four minutes remaining as Al Raheb headed home Mohammed Massad's cross, but it proved just to be a consolation for the home side.