(CNN) -- Defending champion Novak Djokovic eased through to the last 16 of the Indian Wells Masters on a bad day for U.S. men's hopes, while leading female players Maria Sharapova and Caroline Wozniacki moved closer to a semifinal showdown.
World No. 1 Djokovic made light work of big-serving South African 29th seed Kevin Anderson, winning 6-2 6-3 to set up a clash with 45th-ranked Spaniard Pablo Andujar in the fourth round.
"He's very aggressive on the return games. He has a great serve, as you can imagine for his height, so I had to return well. I had to just be patient, and wait for my chances," Serbia's Australian Open champion told the tournament's official website.
The five-time grand slam winner has a clear run to the final following the shock early exit of fourth seed Andy Murray, who he beat in the Melbourne title match in January. In the other half of the draw, last year's runner-up Rafael Nadal faces a potential semifinal against longtime rival Roger Federer.
American No. 1 Mardy Fish, drawn in Djokovic's half of the field for the two-week event, was upset by Australian qualifier Matthew Ebden on Monday. The eighth seed, beaten in the 2008 final by Djokovic, lost 6-3 6-4.
The 24-year-old Ebden, ranked 91st, will next face another American in big-serving 11th seed John Isner -- who beat Argentine No. 22 Juan Monaco 7-5 7-5.
Former world No. 1 Andy Roddick joined Fish in exiting the U.S. hard-court tournament, where he was runner-up in 2010.
The American lost 6-3 4-6 6-2 to Czech seventh seed Tomas Berdych, who will next face Spanish No. 12 Nicolas Almagro.
In the women's draw, three-time grand slam winner Sharapova survived a late rally from Romanian Simona Halep to win 6-3 6-4 and reach the last 16.
"I thought I played extremely well the first four or five games of the second set, almost too good in a way," said 2006 champion Sharapova, who led 5-0 before Halep responded. "Then I felt I almost started going for a bit too much."
The former world No. 1 will play Italy's Roberta Vinci in the fourth round, following the 21st seed's battling 6-7 (5-7) 6-0 6-4 victory over Slovakian No. 16 Dominika Cibulkova.
Defending champion Wozniacki, who lost her spot at the top of the world rankings to Australian Open champion Victoria Azarenka after the Melbourne grand slam, recovered from losing the first set to beat Sweden's Sofia Arvidsson 3-6 7-5 6-2.
"I knew it would be a tough match," the fourth seed said. "I have known Sofia since I was 12 or 13.
"We had the same sponsor and practiced and played together all the time. But I fought for every point and made it through -- I'm happy to be through this one."
The Dane set up a clash with fellow former world No. 1 Ana Ivanovic, after the 15th-seeded Serb eventually earned a 6-7 (8-10) 6-3 6-2 win over Kazakhstan's Ksenia Pervak.
Russian No. 30 Nadia Petrova avenged last year's U.S. Open defeat to eventual champion Samantha Stosur by recording a 6-1 6-7 (6-8) 7-6 (7-5) success against the Australian.
Their encounter at 2011's final grand slam was the longest women's match in the tournament's history, and this match also a marathon, lasting two hours and 46 minutes.
Petrova will next play 20th-seeded compatriot Maria Kirilenko, who beat Spain's Lourdes Dominguez Lido in round three.