World No. 1 Serena Williams reached the semi-finals and British second seed Andy Murray booked a quarter-final berth with straight-set triumphs Tuesday at the WTA and ATP Miami Masters.

Williams defeated Chinese fifth seed Li Na 6-3, 7-6 (7/5) while Murray downed Italian 16th seed Andreas Seppi 6-2, 6-4 at the $8.5 million hardcourt tournament.

World No. 1 Novak Djokovic of Serbia meets German 15th seed Tommy Haas in a later fourth-round match.

Breaking Li three times in each set, Williams fell behind in the second set before roaring back to hold off Li, taking the last point off the Chinese's star's serve to end matters after one hour and 50 minutes.

"It's good to be able to at least come back," Williams said. "I like to believe that I try to be a solver. I just try to do things different if something is not working.

"She played such a good tie-breaker. It was important for me to win that."

Williams had three aces and six double faults to one ace and seven double faults for Li.

"I just can't hit any more double faults," Williams said. "It's embarrassing and unprofessional. I hit about 50 in one game and it was just outrageous. It was like at this point I shouldn't be a professional tennis player.

"That was my goal -- I'm not hitting any more double faults."

Williams improved to 7-1 against Li with her sixth victory in a row, Li's only win coming at Stuttgart in 2008.

"She has such fight," Williams said of Li. "She never quits and I think that we have a lot of that similar."

Williams, trying to become the first six-time winner in Miami history, will face either defending champion and fourth seed Agnieszka Radwanska of Poland or 30th-seeded Belgian Kirsten Flipkens, who meet later, in the semi-finals.

Williams won Miami titles in 2002, 2003, 2004, 2007 and 2008. The 15-time Grand Slam champion also captured last year's US Open, Wimbledon and Olympic crowns.

Li made a strong return to the tour at Miami after an ankle injury suffered in losing the Australian Open final. Li said the ankle felt "100 percent" after the match but wished she could have served better against Williams.

"She's best player in the world," Li said. "If you couldn't hold, she never give you chance again. I still have to see the positive way. I played well so I should be try to be ready for clay court season."

Scotsman Murray, the 2009 Miami winner who lost to Djokovic in last year's Miami final, needed only 86 minutes to book a date in the last eight against the winner of a later match between French sixth seed Jo-Wilfried Tsonga and Croatian ninth seed Marin Cilic.

"Today I served well," Murray said. "You know, when I was down in games I served pretty good, too.

"That can change from day to day, but I just keep working on it each day. Focusing hard on each serve specifically."

In the men's draw Spanish third seed David Ferrer advanced to the quarter-finals with a 6-4, 6-2 victory over Japan's 13th-seeded Kei Nishikori.

Ferrer won 84 percent of his first-serve points and 5-of-9 break chances to eliminate Nishikori and book a last eight-date against Austria's Jurgen Melzer, who defeated Spain's Albert Ramos 2-6, 6-3, 6-3.

Fifth-ranked Ferrer improved to 3-2 in his meetings with Nishikori, having avenged a round-of-16 loss at the Olympics by defeating the Japanese player in the fourth round of this year's Australian Open.

French eighth seed Richard Gasquet outlasted Spanish 10th seed Nicolas Almagro 6-7 (3/7), 7-5, 7-6 (7/3) and will next face Czech fourth seed Tomas Berdych, who dispatched US 17th seed Sam Querrey 6-1, 6-1.