Raonic will next face Slovakian Lukas Lacko, who beat qualifier Edouard Roger-Vasselin of France 7-5, 6-4.
“He doesn't have anything to lose,” Raonic said. “As usual, I'll focus on my serve. He's a very dangerous and powerful player so I will have to play a tight, disciplined game.”
In other matches, sixth-seeded Nicolas Almagro of Spain also advanced to the quarterfinals with a 6-4, 6-2 win over Horacio Zeballos of Argentina.
Defending champion and local favorite Kei Nishikori, who beat Raonic in last year's final, beat Spaniard Feliciano Lopez 7-6 (4), 6-0 and will face Almagro on Friday.
Top-seeded Juan Martin del Potro will play Alexandr Dolgopolov of Ukraine in the quarterfinals on Friday.