Benzema's misfiring Al Ittihad beaten in Asian Champions League
The current Saudi Arabian champions, struggling in the Saudi Pro League, went into the match in Erbil boasting a 100 percent record in Group C after defeating Air Force Club 1-0 in Jeddah last month.
However, goals at the Franso Hariri Stadium from Ali Jasim and Mohannad Abdulraheem pulled the hosts to within two points of the group leaders after four matches.
Back-to-back Asian champions in 2004 and 2005, Ittihad fell behind to the dominant home side one minute before half-time, when Jasim fired home Abdulraheem's cut-back.
Jasim had earlier hit the base of the post with a shot, while he also had a volley tipped over the Ittihad crossbar by Saudi goalkeeper Abdullah Al Maayouf.
Things went from bad to worse for Ittihad not long into the second half, with Abdulraheem sending in a close-range volley from Ibrahim Bayesh's low cross.
Although on form in Asia, Ittihad have been out of sorts in the Saudi Pro League. They have not won in five matches to slip to sixth after 12 rounds, with speculation manager Nuno could be on his way out of the club.
Last season, the former Wolverhampton Wanderers and Tottenham Hotspur manager guided Ittihad to a first Saudi league title in 14 years.
The Air Force Club versus Ittihad encounter was the earliest kick-off on Monday's full programme of Asian Champions League fixtures.
The group stage, which this year returned to a home-and-away format for the first time since early 2020, runs until mid-December, with the 10 pool winners and the six best second-placed teams advancing to the knockout rounds starting in February.
The final takes place, across two legs, in May.