Australia broke the deadlock at Allianz Stadium by way of an own goal in the 54th minute on Friday night before withstanding a late South Korean challenge in front of 37,199 fans.
Their victory over the world No.19 outfit is their first of the year following a disastrous SheBelieves Cup campaign in February.
The Matildas had left the US-based tournament without a single point and slumped to No.16 in the world, their equal-worst position in the history of the FIFA world rankings.
It was also Australia's first win over South Korea since their heartbreaking Asian Cup quarter-final loss in 2022.
"It was really critical to win and to win in a clean sheet makes it even better," interim Matildas coach Tom Sermanni said.
"It's no secret that the SheBelieves wasn't a great tournament for us.
"The key thing when we come up against Asian teams of Japan, Korea, China's quality, we can't afford to sit back and just absorb pressure.
"We've really got to go aggressively and really try to close them down and to make them uncomfortable."
Caitlin Foord helped spark the goal when she won the ball back in Australia's half and broke away from the pack to pass off to Emily van Egmond on the left wing.
Van Egmond sent a slicing cross towards goal before Lim Seon-Joo intercepted with a header, only for the ball to be deflected into the Korean net past the outstretched arm of goalkeeper Kim Min-Jeong.
Mary Fowler came on for Tameka Yallop in the 72nd minute and almost scored seven minutes later when her left-footed shot missed by centimetres.
South Korea burst to life in the final 20 minutes of regulation time, with Shin Na-Yeong almost equalising with a header.
But Australia's goalkeeper Teagan Micah, standing in for injured Mackenzie Arnold, held her nerve to keep the clean sheet.
Foord had the best opportunity in the first half, testing keeper Kim Min-jeong in the 45th minute after a scorching run down the corridor.
The powerful Arsenal forward had earlier sent a scare through the Matildas camp, already without a raft of stars, when she went down in agony in the 20th minute.
Foord had gone face-first into the back of opposition Choe Yu-ri's head.
But she was able to return to the game, having only suffered a bleeding nose.
Australia had lost No.1 keeper Arnold just hours before kick-off to an arm injury picked up in training.
Arnold joins Ellie Carpenter (ankle), Hayley Raso (thigh), Katrina Gorry (ankle) and captain Sam Kerr (knee) on the sidelines.
Gorry had withdrawn ahead of the international window while Carpenter and Raso were ruled out earlier in the week with pre-existing injuries.
Kerr was flanked by the injured quartet on the sidelines at Allianz Stadium in her first Matildas camp since rupturing an anterior cruciate ligament in January last year.
The superstar striker, who avoided being stripped of the Matildas captaincy following her high-profile UK court case in February, was met with thunderous applause when shown on the stadium's big screens.
Australia will play South Korea again on Monday at Newcastle's McDonald Jones Stadium.
The match should be the last under Sermanni, with Football Australia keen to have Tony Gustavsson's permanent successor in place by mid-year.
"I thought it was supposed to be a short time, but I'm still here," Sermanni joked.
Lyon coach Joe Montemurro is the clear front runner for the position, though he is contracted for next season.
Western United coach John Aloisi looms as an outside chance, after leading a youth-filled team to second place on the A-League Men table.
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