MELBOURNE, Australia — Venus Williams has reached the fourth round at a Grand Slam tournament for the first time since Wimbledon in 2011, coming back from a set and a break down to beat Camila Giorgi 4-6, 7-6 (3), 6-1 on Saturday.

The seven-time major winner couldn't contain her delight after the win on Margaret Court Arena, beaming a smile as she turned to wave to all sides of the stadium and then moved to the music blaring over the loud speakers.

The 34-year-old Williams next faces sixth-seeded Agnieszka Radwanska, a semifinalist here last year and Wimbledon finalist in 2012, who advanced with a 6-0, 7-5 win over Varvara Lepchenko.

Williams was diagnosed with an auto-immune condition called Sjogren's syndrome in 2011, which can cause joint pain and saps energy. Since Wimbledon that year, she has missed two majors and made first-round exits in four others, including the 2014 Australian Open.

She was only two points from a third-round departure in the second set, serving at 30-30 in the ninth game, before working her way back into the contest. Giorgi contributed to her own demise with 16 double-faults.

"Well, this old cat has a few tricks left," Williams said in her on-court interview. Being back into the fourth round, "feels fantastic especially when things happen in your life and it's not in your control, so it definitely feels awesome to be here, and I don't want to leave it at that. I'll try to keep going."

Top-ranked Serena Williams was playing on the adjoining Rod Laver Arena against Elina Svitolina on Saturday, also aiming to make the fourth round.

The winner of that match will play No. 24 Garbine Muguruza, who beat Timea Bacsinszky 6-3, 4-6, 6-0.