Defender Cornthwaite, who plays for K-League side Chunnam Dragons and was only brought into the squad after a series of injuries, pounced on a loose ball in the box to complete a come-from-behind victory in Hwaseong.
Australia have had just one win in four games in the final round of FIFA World Cup™ qualifying, but they will enjoy their success which came through Nikita Rukavytsya, who cancelled out Lee Donggook's early strike, and Cornthwaite's late winner.
Korea Republic had climbed to the top of their qualifying group, and they looked on course to see off one of their biggest regional rivals after Donggook volleyed Lee Seunggi's cross past the diving Mark Schwarzer on 11 minutes.
Aussies storm back
But Australia evened things up moments before half-time, as Rukavytsya converted a Tommy Oar pass from the right side of the box. Both sides began the second half slowly before the game opened up in the final 20 minutes. In the 70th, Hwang Jinsung's diving header bounced right at Australian goalkeeper Schwarzer.
Two minutes later, visiting captain Lucas Neill nearly put his side ahead, but Kim Youngkwang in the South Korean goal kept out his close-range header. At the other end, Schwarzer was equal to another volley from Donggook.
When Australian substitute Tom Rogic's hard, left-footed strike in the 84th minute went right at Kim in goal, the teams appeared to be headed for a draw. But in the 87th minute, Cornthwaite capitalised on a mad scramble deep in the South Korean penalty area, when Eli Babalj's shot after a free-kick hit the right post and bounced off goalkeeper Kim.
As the ball rolled along the goalline toward the opposite post, the unmarked Cornthwaite stepped in and calmly put it in the back of the net. Australia's next FIFA World Cup qualifier is at home against Oman on 26 March, while Korea Republic will host Qatar on the same date.