MELBOURNE, Australia — For a full two sets and nine games, Roger Federer was the picture of poise, picking up half-volleys with vintage panache and placing winners past Andy Murray from Britain.

Then, in the bounce of a ball — or two bounces of the ball, depending on opinion — the 17-time major winner from Switzerland was transformed back into the vulnerable, 2013-edition Federer.

After breaking Murray to get a chance to serve for the match Wednesday night and a spot in the Australian Open semifinals for an 11th consecutive year, Federer dropped serve. He recovered and jumped to a 5-2 lead in the tiebreaker, but then Murray rallied and won six of the last seven points to prolong the quarterfinal.

After wasting a handful of break-point chances in Murray’s next service game, which lasted almost 19 minutes, Federer finally wore down the Wimbledon champion 6-3, 6-4, 6-7 (6-8), 6-3 to set up a semifinal showdown with top-ranked Rafael Nadal from Spain.

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Nadal lost the first set and faced set points in the third, getting a reprieve when first-time quarterfinalist Grigor Dimitrov pushed a forehand wide in a tiebreaker. Despite a painful blister on the palm of his left hand that hampered his serve, Nadal advanced 3-6, 7-6 (7-3), 7-6 (9-7), 6-2 against the 22-year-old Bulgarian.

Li Na of China advanced to her third Australian Open final and will have to beat Dominika Cibulkova of Slovakia to win her first title at Melbourne Park.

No. 4 Li had a 6-2, 6-4 win over 19-year-old Canadian Eugenie Bouchard in the first semifinal Thursday before No. 20 Cibulkova trounced 2012 Wimbledon finalist Agnieszka Radwanska of Poland 6-1, 6-2.

Li, the 2011 French Open champion, was the only major winner and the highest-ranked player in the semifinals after the fourth-round upsets of Serena Williams, Maria Sharapova and defending champion Victoria Azarenka.