The world number two pushed through the fatigue of an arduous schedule and overcame a 4-3 deficit in the second set where he won the final three games to continue his spectacular run, that has included his second Wimbledon crown and defence of his Olympics singles title.
"I think the conditions here help a little," Murray said.
"It's pretty quick and there are not a lot of long rallies. That helped me tonight. I played the big points well and that was the difference. That comes from winning big matches and making better decisions."
Murray was last defeated by Novak Djokovic in the French Open final in June and will now meet Milos Raonic in the semi-finals after the big-serving Canadian beat Austrian eighth seed Dominic Thiem.
Raonic lost to Murray in the Wimbledon final.
"He's got one of the biggest serves in the game," Murray said. "I'll need to (return) well if I want to win."
Raonic unleashed 17 aces and did not face a break point during the 68-minute match that put him within two wins of his first ATP World Tour Masters 1000 title.
"I've practiced with him many times, so to some extent I have an understanding of his game, like he has of mine," Raonic told the ATP Tour website.
"But it's different come match time, so I did a little bit of studying. I feel like I took that all in and adapted well."
Raonic skipped the Olympics and instead spent time with coach John McEnroe and the two discussed the disappointment of losing to Murray in his first career grand slam final appearance.
"There were some very prolonged discussions about how I can make a difference on that (mental) part," Raonic told ESPN.
"There were certain moments when I was in the (Wimbledon final) and I thought I was really putting out all the intensity mentally. He (McEnroe) told me he felt I missed a few important moments where I could have showed some intensity. I re-watched the match and saw seven key moments.
"If I want to make the steps forward in the big tournaments, that's going to make the biggest difference."
In other quarter-final action, Croatian 12th seed Marin Cilic advanced when compatriot Borna Coric retired with a knee injury after dropping the first set 6-2 while unseeded Bulgarian Grigor Dimitrov beat American Steve Johnson 7-6(8) 6-2. (Reporting by Andrew Both in Cary, North Carolina and Jahmal Corner in Los Angeles; Editing by Frank Pingue/Greg Stutchbury)
source: www.abs-cbnnews.com
