STANFORD - Seven-time Grand Slam champion Venus Williams ousted fourth-seeded birthday girl Victoria Azarenka in straight sets Thursday to reach the quarter-finals of the WTA hardcourt tournament at Stanford.

The 6-4, 7-6 (7/1) triumph kept Williams on course for a possible semi-final showdown with her sister Serena, the world number one and top seed who will take on Ana Ivanovic in the quarter-finals on Friday. “Williams-Williams tomorrow, hopefully,” Venus told the crowd at the campus of Stanford University, where she came out on top in a hard-fought, physical duel with Azarenka that lasted an hour and 42 minutes. “It’s never easy to play Victoria. We’ve always had extremely tough matches, so I expected that tonight as well,” said Williams, who acknowledged that Azarenka may have been at a disadvantage after having a first-round bye.

That meant the match was the Belarussian’s first since her second-round exit at Wimbledon. It was a disappointing result on her 25th birthday for Azarenka, who came into the week ranked 10th in the world but needed to reach the semi-finals to stay in the top 10. A left foot injury sidelined her for three months this year before she returned to action at the Wimbledon tuneup event at Eastbourne. The former world number one, who owns two Australian Open titles, didn’t go quietly. She gamely fought off two match points in the 12th game of the second set to force the tiebreaker, but from there it was all Williams.

The 34-year-old American won the first point of the tiebreaker on her own serve, then fired two forehand winners to take the next two points on Azarenka’s serve and never looked back. Azarenka double faulted to give Williams a 6-1 lead, and the American held on to win the next point — firing over a running forehand that Azarenka could only belt back into the net. Williams had come on strong late in the opening set as well, sealing the frame with a service break in the final game.  Williams next faces eighth-seeded German Andrea Petkovic, who booked her quarter-final berth on Wednesday.

Earlier Thursday, fifth-seeded Ivanovic cruised past Canadian qualifier 6-1, 6-1 in just 54 minutes to book her third meeting this year with Serena Williams.

Ivanovic, a former world number one herself, downed the American at the Australian Open, a defeat that Serena avenged in Rome. The two have never played each other this many times in one season. “It’s a good sign,” Ivanovic said. “It means we’re getting further into the tournaments to play each other.”

In other matches on Thursday, third-seeded Angelique Kerber of Germany got past American Coco Vandeweghe 7-6 (7/4), 0-6, 6-2 to book a quarter-final with rising Spanish talent Garbine Muguruza — a 6-4, 6-4 winner over Slovakian Daniela Hantuchova 6-4, 6-4.