BRISBANE, Australia -- Serena Williams had a tough win over the woman she's predicting will one day top the rankings, setting up a semifinal match at the Brisbane International against current No. 1 Victoria Azarenka.
The reigning Wimbledon, U.S. Open and Olympic champion showed plenty of emotion on key points in a heavy-hitting duel with Fed Cup teammate Sloane Stephens on Thursday before winning 6-4, 6-3.
Williams converted both break points and fended off one break chance against her in each set, later saying Stephens had the potential to be "the best in the world one day."
Stephens was hitting the ball hard and cleanly, and got the better of some powerful rallies, but lacked experience in the two key moments -- giving up a set point after wasting a game point on her own serve in the first and dropping serve in the eighth game of the second set.
The 19-year-old Stephens accepted the warm praise from Williams, her childhood idol.
"To have someone like that who I think is one of the greatest players to ever play the game say that about you is really nice," Stephens said. "I lost to the best player in the world today, so, you know, it's good."
Williams has an 11-1 record against Azarenka and was 5-0 against the 23-year-old Belarussian in 2012, including the U.S. Open final.
Olympic and U.S. Open champion Andy Murray was pushed before winning his opening match 6-1, 5-7, 6-3 against Australian qualifier John Millman, who finished last year ranked No. 228.
The third-ranked Murray, the defending Brisbane champion, clutched at his stomach after missing a forehand in the third game of the second set and later had to save four set points before Millman tied the match at one set apiece.
Murray recovered from his lapse, got the only break in the deciding third set and finished off by holding serve at love. He'll meet Denis Istomin of Uzbekistan, a 7-5, 7-5 winner over former No. 1 Lleyton Hewitt, in the quarterfinals.
"For a first match of the year, that was a perfect match in many ways to go through some tough moments, a lot of long rallies, close games, and important points," Murray said. "It was great to play in an atmosphere like that for the first match of the year, to get back into the swing of playing in front of large and loud crowds.
"No matter how much you practice, you can't replicate those sorts of atmospheres."
In the other men's second-round matches, Grigor Dimitrov of Bulgaria upset No. 2-seeded Milos Raonic of Canada 6-3, 6-4 and No. 7 Jurgen Melzer of Austria had a 6-5, 7-6 (4) win over David Goffin of Belgium.
The women's semifinals are set for Friday, with Williams getting the least recovery time.
She seemed to have trouble with her right calf muscle midway through the second set against Stephens, knocking her lower leg three times with her racket before she served at 40-0 in the fifth game, but later said she didn't have any injury concerns.
Azarenka started 2012 on a run, winning the Sydney International and the Australian Open -- her first major -- and gaining the No. 1 ranking during a 26-match winning streak.
But after a first-round exit in the French Open, Williams finished 2012 as the most dominant woman on tour. She has won 34 of her last 35 matches, including titles at Wimbledon, the London Olympics, the U.S. Open and the WTA Championships.
With the Australian Open starting on Jan. 14, and neither Azarenka nor Williams playing another tournament before then, Friday's semifinal shapes up as a classic.
"I'm going up against the world's greatest tomorrow. She had a fabulous year," the third-ranked Williams said of Azarenka. "I feel like I have nothing to lose. She's playing so well, she won I think in 20 minutes today. I have a lot of work to do tomorrow."
Azarenka actually took 68 minutes to win her quarterfinal match. And she was looking forward to a chance to beat Williams, a 15-time major winner, before the first Grand Slam event of 2013.
"Well, it's a tough match, there is no question about it," Azarenka said. "It's going to be a great test for the Australian Open."
Azarenka and Williams are the only two seeded players still in contention in Brisbane after No. 36-ranked Anastasia Pavlyuchenkova of Russia beat No. 4 Angelique Kerber of Germany 7-6 (3), 7-6 (3) in the first of the quarterfinals, her second win over a top 10 player this week after defeating 2011 Wimbledon champion Petra Kvitova in the first round.
Pavlyuchenkova will play Lesia Tsurenko of Ukraine, the lucky loser from qualifying who got into the main draw when No. 2-ranked Maria Sharapova withdrew because of a sore right collarbone. Tsurenko had a 6-3, 6-4 win over Daniela Hantuchova of Slovakia.