The 25-year-old Murray had his service broken for only the second time while serving for the match. But he broke back immediately in the next game to clinch a quarterfinal victory.
Murray, who ended a 76-year winless streak by British men in majors by winning the U.S. Open last year, will play either Roger Federer or Jo-Wilfried Tsonga in a semifinal on Friday.
Defending champion Novak Djokovic plays No. 4-seeded David Ferrer in the other semifinal.