Former Bayern Munich, Atletico Madrid and Juventus forward Mandzukic, who was part of the Croatia side who finished runners-up at the 2018 World Cup, headed in a fifth-minute cross from Almoez Ali to give the hosts the lead at the Abdulla bin Khalifa Stadium in Doha.
Mandzukic got plenty of help from the Persepolis defenders though, as they were busy protesting an alleged foul even as Ali chipped the ball from just outside the penalty area.
Despite the early setback, the visitors, who boast a fan following of more than 40 million in Iran, failed to get their defence right as the home side consolidated the lead in the 13th minute.
North Korea forward Han Kwang-song took advantage of another Persepolis mistake by pouncing on a loose ball on the edge of the box before passing the ball to Brazilian Edmilson who scored with a low shot.
The Tehran side barely made an impact in the first half, but ex-Celtic striker Anthony Stokes tested the Al Duhail defence on his club debut a couple of times after the break.
In Group D, Qatar’s Al Sadd and Saudi Arabia’s Al Nassr figured in an entertaining 2-2 draw at the Prince Faisal bin Fahad Stadium in Riyadh.