The Qatari club, coached by former Saudi Arabian boss Marcos Paqueta, had a number of chances but the only goal of the game came from the visitors.
After 62 minutes, Ahmed Ajab headed home.
In the group’s other game, Pakhtakor of Uzbekistan moved into second place with a comfortable 2-0 win at home to Arbil. The defeat was the first for the Iraqi team.
Both goals came soon after the restart as Ilhomjon Suyunov and Alexander Geynrikh put the game out of the visitors’ reach.
1: Al Qadsia 7 2: Pakhtakor 4 3: Al Gharafa 2 4: Arbil 2
