Sandjar Shaakhmedov netted 20 minutes from time to earn AGMK a point against an Al Hilal side that was playing in the competition for the first time since being kicked out last season.
A series of positive COVID-19 tests during last year's group phase had left the 2019 champions incapable of selecting a full squad, leading to their expulsion and the end of their title defence.
Their return started inauspiciously when goalkeeper Abdullah Al Maiouf gifted AGMK their opener inside 11 minutes when his scuffed attempt to clear was presented to Zafar Polvonov and he rolled the ball home.
But an own goal by Sardor Rakhmanov under pressure from Bafetimbi Gomis 16 minutes later pulled Al Hilal level and Luciano Vietto put the Saudis in front from close range nine minutes before the break.
Shaakhmedov then pounced after Al Maiouf had parried the ball into his path 20 minutes from time to earn AGMK a point in the group A clash.
Al Hilal and AGMK are joined on one point following the first round of matches after another tournament debutant, Istiklol of Tajikistan, held Shabab Al Ahli from the United Arab Emirates to a 0-0 draw.
In group C, Iran's Esteghlal handed Al Ahli from Saudi Arabia a 5-2 thrashing in Jeddah thanks to an impressive second half showing that included a late brace for Mehdi Ghayedi.
The club from Tehran were joined at the top of the early group standings by Qatar's Al Duhail, who handed Al Shorta from Iraq a 2-0 defeat.