Murray, who faces eighth-seeded Gilles Simon in the next round, fought back from a break of serve in the second set and won the last four games.
Simon beat Jeremy Chardy 6-4, 6-3.
Defending champion Tomas Berdych also advanced, hitting 10 aces in a 6-0, 3-6, 6-3 victory over Andreas Seppi. The third-seeded Czech will take on Gael Monfils for a spot in the semifinals.
Milos Raonic of Thornhill, Ont., faces Italy's Simone Bolelli later Thursday.