Raonic beat Australia's Marinko Matosevic 7-6 (3), 4-6, 6-4 on Thursday to open his autumn swing through Asia despite failing to convert on 15 of his 16 break point chances.
The 11th-ranked player in the world survived a demanding 2 1/2-hour match, finally advancing on a break of serve in the final game.
"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)."
Raonic, from Thornhill, Ont., had 21 aces and faced only four break points on his serve, saving three of them.
"It was a little bit frustrating," he admitted. "But he played well on a lot of those break points so I can't always blame myself.
"I couldn't ask any more, I just told myself to hang in there and keep going."
Raonic got a break point to go his way in the final game of the match. Matosevic saved three match points but was finally defeated on the fourth opportunity.
"After missing on so many break points I finally just went for it. I'd rather play that way that letting him dictate," Raonic said.
"I did a lot of things well but I had to keep plugging away. I did that was able to finally break at the end."
Raonic, the third seed at the tournament, will next face Spain's Feliciano Lopez a month after beating the sixth seed in the U.S. Open third round.
"It will be very different conditions, this being indoors," Raonic said of the rematch. "But I think I can find a solution within myself, I just have to focus on what I need to do."
Raonic had a bye in the first round.
He began his ATP autumn stretch after Canada's Davis Cup semifinal loss to Serbia in Belgrade.
Raonic is the first Canadian man achieve an ATP top 10 ranking and is bidding for a place in the eight-man year-end final in London in November. He will need several weeks of good results if he is to rise from his current standing of provisional 11th in the season points race.
Gilles Simon of France, the 2009 champion and last year's runner-up, also reached the quarter-finals 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."
Also, Yen-hsun Lu of Taiwan ousted eighth-seeded Lukas Rosol of the Czech Republic 6-3, 6-2 to be the last Asian in the draw, and fifth-seeded Mikhail Youzhny of Russia won through.
— With files from The Associated Press.