The Koreans, who sealed top spot by virtue of their superior goal tally over the three group fixtures, will return to Stadium Australia on Saturday for a quarter-final against a third-placed team from one of the other opening-round groups.
The Matildas, meanwhile, will have to travel across Australia to play either North Korea or reigning champions China in the last eight at Perth Rectangular Stadium on Friday.
South Korea, runners-up at the last Asian Cup in 2022, opened the scoring in the 13th minute when Mun Eun-Ju latched onto an inch-perfect pass from Jeon Yu-Gyeong and slid the ball past Mackenzie Arnold.
Kennedy bundled the ball over the line in a goalmouth scramble in the 32nd minute, however, and Sam Kerr drilled home a second in stoppage time at the end of the first half to put the Matildas in front at halftime.
Kim Shin-Ji equalised from the penalty spot six minutes into the second half, and her fellow substitute Kang Chae-Rim threaded the ball into the far corner from the edge of the box to put the Koreans back in front three minutes later.
Roared on by a crowd of 60,279, Australia pressed forward in the last 20 minutes, desperately seeking the two goals they needed to top the group and ensure they would stay in Sydney for as long as they remained in the tournament.
Midfielder Kennedy got one with a powerful shot into the roof of the net eight minutes into stoppage time, but there was not enough time for another.
"You never doubt the confidence and the fight, but we need to manage games better," said Australia coach Joe Montemurro.
"We were very patchy tonight and I think when you play against a quality team, and when they can retain the ball, you're not going to get the result you want."
Check out all the match stats here.
In the other Group A match, the Philippines beat Iran 2-0 with goals from Sara Eggesvik and Chandler McDaniel at a rain-soaked Gold Coast Stadium to keep alive their hopes of progressing as one of the best third-placed teams.
Iran, who continued to play in the tournament despite war breaking out back home, sang their national anthem and gave it everything they had, but will exit the tournament winless and without a goal.