Murray defeated Ivo Karlovic 7-6 (9-7), 6-4 in a match that had just one service break. Murray lost only nine points in 11 service games and used the lone break of the match to win the second set.
Murray won 85 percent of the points on serve, including 29-of-33 -- 88 percent -- when he was good on his first serve.
Local favorite Tatsuma Ito edged fifth-seeded Nicolas Almagro 7-6 (7-4), 7-6 (7-5). Ito dropped serve just once, saving six other break points. He also was in control when he landed his first serves, winning 86 percent of those points.
No. 6-seeded Milos Raonic got by Radek Stepanek 6-4, 6-4 and eighth-seeded Kei Nishikori edged Go Soeda 4-6, 6-2, 6-3 in a battle of Japanese players.
Qualifiers Marco Chiudinelli and Dmitry Tursunov also advanced to the second round. Tursunov defeated Bernard Tomic 6-4, 7-5 while Chiudinelli stopped Martin Klizan 7-6 (7-3), 6-2.
Also Tuesday, Jeremy Chardy eliminated Yuichi Sugita 6-1, 7-5; Marcos Baghdatis eked out a 7-6 (7-3), 7-5 decision over Sergiy Stakhovsky; Tommy Robredo handled Jarkko Nieminen 6-2, 6-4; and Alejandro Falla topped Thomaz Bellucci 7-5, 6-2.