MELBOURNE, Australia (AP) — Serena Williams saw that older sister Venus was progressing to the fourth round at a Grand Slam tournament for the first time since 2011 and it inspired her own comeback win on Saturday at the Australian Open.

Top-ranked Serena Willliams made a lackluster start to her third-round match against No. 26-ranked Elina Svitolina on Rod Laver Arena — knowing when she walked out that Venus was down a set and a break on a nearby court — but picked up her game after realizing her sister had recovered and was advancing with a 4-6, 7-6 (3), 6-1 win over Camila Giorgi.

Svitolina “kept hitting winners in the first set, there’s not much I can do. Then I saw (Venus’) score and thought ‘Wow she’s winning, well I can do better,’” Serena Williams said after her 4-6, 6-2, 6-0 win. “We always motivate each other.”

She’ll have to be at the top of her game in the next round she meets No. 24 Garbine Muguruza, who beat her in the second round at the French Open last year. Muguruza defeated Timea Bacsinszky 6-3, 4-6, 6-0.

Venus Williams couldn’t contain her delight after her 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. She said the sibling relationship, and rivalry, helped both of the Williams sisters.

“I’ve been motivated by Serena though since day one, since ‘97. She’s always been I think someone that anyone can learn from. The way she faces her life, the way she is fearless on the court,” Venus Williams said.

“I probably take it a lot more to heart because she’s my sister and we’ve had the fortunate relationship to be able to motivate each other and grow from each other. I don’t think I could have done the things I’ve done without her.”

The 34-year-old, seven-time major winner 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.

Venus Williams was diagnosed with an auto-immune condition called Sjogren’s syndrome in 2011, which can cause joint pain and saps energy. In the 13 Grand Slam tournaments after her fourth-round appearance at Wimbledon that year, she skipped two 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 against Giorgi, serving at 30-30 in the ninth game, before working her way back into the contest. Giorgi also had a chance to serve for the match but couldn’t hold. The Italian player contributed to her own demise with 16 double-faults.

“Well, this old cat has a few tricks left,” Venus 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 like to win titles, whether it’s a smaller event or a big event. That’s what I play for. So, yes, great, it’s great to be in the second week but is fourth round my goal when I come to these tournaments? No.”

Eighth-seeded Milos Raonic reached the fourth round at a fourth consecutive Grand Slam tournament, firing 22 aces in a 6-4, 6-3, 6-3 win over Benjamin Becker of Germany.

Raonic became the first Canadian man to reach a Grand Slam semifinal at Wimbledon last year after making it to the quarterfinals at the French Open.