City looked in dire straits on Tuesday night when the Thai club's Serbian midfielder Goran Causic headed home the opening goal in the 72nd minute.
But with Socceroos coach Tony Popovic watching at AAMI Park, captain Aziz Behich teed up substitute Elsaban Rashani to equalise in the 84th minute before young striker Max Caputo scored a 97th-minute winner.
Aurelio Vidmar's City (three points) sit seventh after two losses and Tuesday's win, ahead of eighth-placed Buriram on goal difference.
This was City's first win in Asia since beating the same opponents 2-0 in October 2023.
"Two years ago, I was a part of the team that didn't get out of the group stage - we picked up three points (total)," Caputo, 20, said.
"And to pick up our first three points tonight at home in front of the fans, it's a good feeling, good for the club, and we'll bring this confidence into the next game."
With five games to go, City are back in the mix to qualify for the round of 16, with eight of the 12 teams in the east division qualifying for the knockouts.
"We felt like we were progressing in this tournament and this competition, and that should give us a lot of confidence moving forward," Vidmar said.
Mark Jackson coached Buriram, 12 days after walking out on the A-League's Central Coast Mariners, while ex-City defender Curtis Good and former Socceroos midfielder Kenny Dougall started.
In first-half injury time, Causic headed home, but the goal was chalked off for offside after a VAR review.
City's Harry Shillington (concussion) was substituted in the 59th minute along with Samuel Souprayen (hamstring).
Buriram struck when they swung in a corner and striker Supachai Chaided bicycle-kicked the ball into the path of Peter Zulj.
Zulj's shot forced Patrick Beach into a terrific save, but the ball spilled out to Causic, who took a touch and slammed it home.
City struggled to create anything until Behich burst down the left then cut the ball back for Rashani to drive it into the back of the net.
Then in the dying minutes, Nathaniel Atkinson whipped a terrific ball into the back post for Caputo to turn home the winner.
"Very disappointing end to the game for us," Jackson said.
"For long periods, we had a strategy and a game plan that was working, and we went one goal ahead and we probably didn't manage the momentum of the game from that moment.
"Ultimately, that cost us."
City return to A-League action against Perth Glory on Saturday, when they expect to regain Mathew Leckie (knee).
They are back in the ACL Elite when away to Japanese club Machida Zelvia, home of Socceroos striker Mitch Duke, on November 4.
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