Murray, seeded second, won 6-1 6-2 and will next play Belgian David Goffin - a warm-up for this month's likely meeting in the Davis Cup final.
British number two Aljaz Bedene earlier lost 6-3 7-6 (7-3) to American 13th seed John Isner.
Rafael Nadal beat Lukas Rosol 6-2 6-2, with Roger Federer also progressing.