Melbourne, Australia (SportsNetwork.com) - The Williams sisters are through to the fourth round at the Australian Open, but both top seed Serena and No. 18 seed Venus had to rally from a set down Saturday.

Serena, a five-time Aussie champion, came back to down 26th-seeded Ukrainian Elina Svitolina, 4-6, 6-2, 6-0. Venus, a seven-time Grand Slam champion, topped talented Italian Camila Giorgi, 4-6, 7-6 (7-3), 6-1.

It was a rough start for Serena, who fell behind 5-2 in the first set, but then won the next two games. Svitolina came back to hold at love the next game to take the set.

The final two sets were completely different, as the 18-time Grand Slam champion and reigning U.S. Open queen won the first four games of the second and throttled her opponent in the third.

"My next match I'm just going to have a longer warmup, more intense warmup. But as long as I was able to come through today, I can always have an opportunity for tomorrow," Serena said.

There was a brief opening for Svitolina in the third game of the final set, but she blew a pair of break point chances.

Revenge could be a factor in Serena's next match. She was the defending champion headed into the 2014 French Open, but lost in the second round to Spain's Garbine Muguruza.

Muguruza, the 24th seed here, set up her match with Serena with a win over Switzerland's Timea Bacsinszky, 6-3, 4-6, 6-0.

"It was a good loss," Serena said of her loss to Muguruza. "As angry as I was, it was the best loss I had the whole year last year. Had a lot of them. But that one in particular made me realize what I needed to work on. It opened my eyes towards a lot of things."

Venus was two points away from losing the match to Giorgi, but then rallied. Giorgi double-faulted 16 times.

This will be the first time Venus has reached the round-of-16 at a major since Wimbledon 2011.

"It's definitely been a lot of work and a lot of learning and a lot of perseverance," Venus said. "It will continue to be that for me. Just have to come to terms with it."

Next up for Venus is sixth seed Agnieszka Radwanska of Poland. The Wimbledon runner-up surged past American Varvara Lepchenko, the 30th seed, 6-0, 7-5.

Also Saturday, 11th seed Dominika Cibulkova defeated 19th seed Alize Cornet, 7-5, 6-2; and Madison Brengle upended fellow American Coco Vandeweghe, 6-3, 6-2.