The former Millwall striker Alistair Edwards was the home hero, coming off the bench to score what proved to be the winning goal in the 72nd minute. Australia beat New Zealand 1-0 in their first game under Venables on Saturday, and are now the only unbeaten team in the Four Nations tournament.
The former England coach said: "We knew we were in for a hard game, but I was really pleased with the players. This team has really come on."
Australia dominated the first half, with the midfielder Paul Trimboli setting up Matthew Bingley for the opening goal. However, South Korea were dangerous on the counter-attack, and the former Leicester goalkeeper Zeljko Kalac pulled off two excellent saves from Kim Hyun Soo and Ko Jung Su. In the second half Edwards extended Australia's lead before Ha Seok Ju pulled one back for South Korea.
In yesterday's other game in Brisbane, Norway beat New Zealand 3-0. Australia play Norway and South Korea take on New Zealand in the matches that conclude the tournament in Sydney on Saturday.
Venables added: "It's early days, but I'm really pleased. We created chances and we defended well against a very good side.
"We've only had four training sessions together, and I thought we did a lot of things better. That is the sort of test we will face if we want to get to the World Cup." Australia must win the Oceania qualifying group before a play-off against the fourth-best Asian side to earn a place at next year's World Cup.
A threat by the trade union representing Australia's players to take strike action this weekend as an extension of a pay dispute was withdrawn after discussions with Soccer Australia, Venables' employers.Reuse content