Guangzhou, coached by World Cup-winning Italian Marcello Lippi, appeared to be heading for victory until Montenegro striker Damjanovic slotted in a cross from Sergio Escudero with seven minutes remaining.
The same pair also combined in the Korean champions' opening goal in the 11th minute when Escudero calmly placed the ball past Guangzhou goalkeeper Zeng Cheng after being set up by Damjanovic.
The Chinese side equalised in the 29th minute, much to the disappointment of the packed house at the Seoul World Cup Stadium, when Brazilian Elkeson headed in a corner for his fifth goal of the tournament.
China international Gao Lin made it 2-1 for Guangzhou, who are trying to become the country's first winner of the region's premier club tournament, by deftly diverting in a low cross just before the hour.
A win for Guangzhou, who will host the return leg on Nov. 9, will make Lippi the first coach to win both the UEFA and Asian Champions League titles.