After a first-round bye, the Canadian had to dig deep in a 2½-hour match that featured lengthy baseline rallies.
"I created my opportunities, but I wasn't converting any," he said. "He was playing so well on a lot of break points, and a few I didn't play well. I just kept plugging away and finally broke him (in the third set)."
Gilles Simon of France, the 2009 champion and last year's runner-up, also reached the quarterfinals when he defeated Bernard Tomic of Australia 6-4, 7-5. The win was his 300th on the ATP tour, and sixth in a row following his title run in Metz last week.
"I feel confident on court, I was playing great tennis in Metz," Simon said. "Now I'm a bit tired and I have to be careful not to get injured because I just came back from injuries."