After a tightly contested opening at AAMI Park, the visitors took the lead in the 37th minute through a stunning first-time strike from Guilherme Bissoli, leaving City with work to do in the second half.
City responded strongly after the break, controlling territory and creating a series of chances.
Daniel Arzani and Aziz Behich went close, while substitutes Max Caputo and Kavian Rahmani injected energy into the attack as City pushed for an equaliser.
With time running out, Aurelio Vidmar made one final change, introducing Ben Mazzeo in stoppage time - a move that would prove decisive.
In a flowing team move in the 95th minute, Nathaniel Atkinson drove forward before Rahmani flicked the ball into the path of player of the match Marcus Younis.
The January signing produced a superb cross to the back post, where Mazzeo rose highest to head home and level the tie.
Tuesday night's result leaves the tie evenly poised at 1-1 ahead of next week's second leg in Thailand, with a place in the quarter-finals on the line.
"I thought it was a reasonably even game," said City coach Aurelio Vidmar.
"I know we left it late, but we managed to find a way, and we certainly deserved that goal. It's now an even tie going into next week."
Younis said: "Tonight shows the character that this squad has. I think we deserved more, but it's nice to head into next week on level terms.
"We had to stay switched on for the full 90 minutes, and I think it's so important that we have that mentality to never give up."
