No. 2 Federer, who took the Indian Wells title three consecutive years beginning in 2004, next will play No. 4 Andy Murray. The 21-year-old Scot defeated Ivan Ljubicic 7-5, 7-6 (6) to run his 2009 match record to 19-1.
The other quarterfinals have No. 1 Rafael Nadal meeting No. 7 Juan Martin del Potro, and No. 3 Novak Djokovic, the defending champion, facing No. 7 Andy Roddick. Both those matches are on Friday.
Federer overcame a lapse in the second set, when he lost a 4-2 lead and then allowed No. 10 Verdasco to break his service to take a 6-5 lead. But the Swiss star came back to break Verdasco in the following game, when Verdasco doublefaulted, hit a forehand long and a backhand long to lose three of the final four points.
Federer then built a 5-1 lead in the tiebreaker and finished it off with a service winner.
“It was difficult,” Federer said. “I wasn’t quite happy with the match, but for a while there, I actually was playing OK. I struggled with my rhythm on the backhand.”
Verdasco said, “I think we didn’t play our best tennis in any moment of the match. I didn’t feel so good tonight. I also don’t think he played his best tennis.”
Murray, whose game appears to be getting better all the time, beat Ljubicic by simply keeping the ball in play. No. 4 Murray hit just 17 winners to 36 by his Croatian opponent, but made only 15 unforced errors to Ljubicic’s 40.
The loss sullied Ljubicic’s birthday; the oldest player remaining in the field, he turned 30.
Murray has won twice already this year, at Doha and Rotterdam.
Heading into Indian Wells, he said, he hadn’t really considered how far he might advance.
“I wasn’t thinking about the semifinals at all,” Murray said. “I was thinking about the first-round match and how I would get through that, and each day working on my game and trying to get a little better.
“I have done that with each match, and with the next match, hopefully I’ll play even better.”
Anastasia Pavlyuchenkova, a 17-year-old from Moscow who’s beginning to look like the next Russian star, continued her run of upsets with a 7-6 (8), 6-4 victory over No. 10 Agnieszka Radwanska. No. 42 Pavlyuchenkova, who knocked off No. 3 Jelena Jankovic in the second round, next faces defending champion Ana Ivanovic.
“I’m very excited now, and more and more every day because I keep winning,” Pavlyuchenkova said. “And it’s some really big achievements for me this week. I beat some really good players.
“I’m very happy, especially today; first time in semis.”
The semifinals appearance will be Pavlyuchenkova’s first in a WTA event.
Ivanovic advanced when her opponent, Sybille Bammer, withdrew because of an injured left shoulder.
“I’m very disappointed because I was playing better and better. Two years ago, I beat Ana here, so it’s frustrating for me,” said Bammer, who hurt her shoulder in practice the previous day.
She said she will have an MRI and then rest “and hope I am fine for Miami.”
Victoria Azarenka plays Vera Zvonareva in the women’s other semifinal on Friday.
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