Home-town hero Craig Goodwin slotted a stunning, long-range strike in the 53rd minute and set up Australia's first goal on the cusp of half-time with a free kick that found Lewis Miller's head and cancelled out Xie Wenneng's 20th minute opener.
Nishan Velupillay then made sure of the win on his international debut with a stoppage time goal in front of a record crowd of 46,291 for a Socceroos match in Adelaide.
After a shock 1-0 home defeat by Bahrain and a 0-0 draw away to Indonesia, the win revived Australia's chances of finishing the third phase of Asian qualifying with a top-two spot and an automatic ticket to the 2026 finals in North America.
"I think we did really well, even in the first half. China were very, very compact," said Saudi-based Goodwin.
"Hats off to the boys, we were 1-0 down and after the first two games with the results we had we could have gone into our shell."
China, who have conceded 12 goals in their three qualifiers so far, remain winless in Group C.
Australia travel to group leaders Japan next week, and the hosts may be unfazed by their threat after what was a mostly scrappy showing in Adelaide.
Popovic started with a 3-4-3 formation and a rejigged 11, with Aston Villa goalkeeper Joe Gauci replacing regular stopper Mat Ryan and Jackson Irvine taking the captain's armband.
China were happy to let the hosts have the ball, and as against Bahrain and Indonesia, Australia could do little with it against a wall of defenders.
The hosts were soon back-pedalling in panic as China's goalkeeper-captain Wang Dalei hoofed a goal-kick down-field.
It found the head of Zhang Yuning, who nodded it into the path of a hard-charging Xie, the winger sliding the ball inside the far post with a quality, left-foot finish.
The goal silenced the home fans but Goodwin rallied them with a curling free-kick from the left flank that Miller rose to thump into the net.
The goal was a measure of redemption for Miller who was pilloried relentlessly after a horror match in Australia's Asian Cup quarter-final loss to South Korea.
Velupillay, developed by Popovic at Melbourne Victory, came off the bench to slot from close range, ensuring the Socceroos head to Japan with optimism.
"This was such an important performance," said captain Irvine.
"We're going to have positive vibes for the next few days going into that tough game on Tuesday."