MELBOURNE, Australia — Push Simona Halep to the brink and she summons her best.

The Australian Open’s top-seeded woman got all she could handle from 20-year-old American Sofia Kenin in the second round before taking the last four games to emerge with a 6-3, 6-7 (5), 6-4 victory that took 2½ hours Thursday.

“I have no idea how I won,” said Halep, the French Open champion. “It’s tough to explain what happened on court.”

A year ago, Halep was a point from being eliminated in two matches but came back each time en route to reaching the final. In the first round this year, she was down a set and a break before turning things around. And this time, against Kenin, Halep trailed 4-2 in the third set and managed to not cede another game.

And that was despite getting what she described as “a little bit injured” in the second set, something that seemed clear from the way she wasn’t always able to run with her usual verve.

“Hopefully,” said Halep, whose No. 1 ranking is up for grabs during the Australian Open, “next round I play better.”

That third-round matchup will be intriguing because it will be against seven-time Grand Slam champion and former No. 1 Venus Williams. And the winner could face Williams’ younger sister, 23-time major champ Serena.

Venus won a three-setter, and in much more emphatic fashion. Pushed to that deciding set by getting broken to end the second, Venus ran away down the stretch, defeating Alize Cornet, 6-3, 4-6, 6-0.

“She was just putting more intensity than me. She was hitting harder, deeper,” Cornet said. “I had a little less energy than in the second set and she took advantage of it and really raised her level.”

Venus, 38, unseeded at a major for the first time in five years, was the runner-up in Australia to Serena in 2003 and 2017.

Serena advanced to the third round by beating 2014 Wimbledon finalist Eugenie Bouchard 6-2, 6-2, reeling off the last five games and 16 of the final 20 points. That match was followed by No. 1 Novak Djokovic’s 6-3, 7-5, 6-4 victory over Jo-Wilfried Tsonga.