Just three points separate the four sides in the group and Gyan's double ensured Al Ain's place at the summit as Sazi suffered their first defeat in this year's competition.
The Ghanaian opened the scoring with 16 minutes gone, with Mohamed Abdulrahman doubling the advantage seven minutes before the break.
Milad Fakhreddini halved the deficit just four minutes later, but Gyan netted his second of the game and third of the group stage 17 minutes from time to seal victory.
That result allowed Lekhwiya to move above Sazi into second in the table on goal difference after strikes from Sebastian Soria and Nam Tae-Hee earned them a 2-0 win over Al Ittihad, who saw Hamad Al Montashari dismissed 10 minutes from time.
Al Shabab's Group A match versus Al Rayyan provided plenty of drama as the hosts twice came from behind to win 4-3.
Two goals from Kalu Uche helped the visitors into a 3-2 lead by half-time, but a quick-fire brace from Rafinha just after the break saw the Saudi outfit complete the comeback.
The win moved Al Shabab up to second in the group, a point behind Al Jazira, whose 100 per cent record was spoiled in a 2-2 draw at last year's semi-finalists Esteghlal.
The visitors twice held the lead through Abdelaziz Barrada, but they were pegged back on both occasions by Mohammad Ghazi Najafabadi and then Hanif Omranzadeh as the Iranians earned their first point of the campaign.
Reigning champions Guangzhou Evergrande continued their strong start to the defence of their title with a 3-1 home win over Jeonbuk Motors, while elsewhere in Group G Melbourne Victory beat Yokohama F. Marinos 1-0.
In Group E, Pohang Steelers came from two goals and a man down to draw 2-2 with Shandong Luneng, while Diego Forlan was on the scoresheet in Cerezo Osaka's 4-0 thumping of Buriram United.
