Venus Williams reached the Australian Open semi-finals for the first time in 14 years with a straight-set win over Russia’s Anastasia Pavlyuchenkova.
Williams, the 13th seed, saw off 24th seed Pavlyuchenkova 6-4 7-6 (7-3) in the first of the quarter-finals.
The 36-year-old American has never won the title, her best effort a runner-up finish to sister Serena in 2003.
She goes on to face unseeded American Coco Vandeweghe, who thrashed Spain’s seventh seed Garbine Muguruza 6-4 6-0.
Vandeweghe, 25, followed up her win over world number one and defending champion Angelique Kerber with a crushing defeat of French Open champion Muguruza.
“I really wasn’t feeling all that great out there, I was feeling kind of nervous,” said Vandeweghe.
“I just tried to play my best, stay within myself, keep my patterns. I fought through a few break points on her serve, kept on the pressure in the first set and then she finally cracked.
“Once I got rolling in the second it was like a freight train. You couldn’t stop it.”
“I’d like to be champion” – Venus
Williams, meanwhile, dropped serve four times against Pavlyuchenkova but was much the stronger in the decisive moments, becoming the oldest woman to reach a Grand Slam semi-final since Martina Navratilova at Wimbledon in 1994.
“I’m so excited. Today was such a hard-fought match. She never let up,” said the seven-time Grand Slam champion.
“It’s wonderful to be here at the start of the year. I want to go further. I’m not happy with this.
“I try to believe. Should I look across the net and believe the person across the net deserves it more?
“This mentality is not how champions are made. I’d like to be a champion, in particular this year. The mentality I walk on court with is: I deserve this.”
On Wednesday, Serena Williams will play Britain’s Johanna Konta at about 02:00 GMT, following the match between Czech fifth seed Karolina Plisokva and Croatia’s Mirjana Lucic-Baroni.