The 23-year-old from Thornhill, Ont., turned in a 4-6, 7-5, 6-3 victory over the Wimbledon winner on Wednesday, the 20th anniversary of his family's emigrating from the former Yugoslavia (now Montenegro) to Canada. Raonic said he got a reminder from his sister of the big occasion, which he credits with changing his life.
"That move for our family has given as much to me as it has to my brother, my sister, and my parents: great educations; great support system that my parents instilled in us was made possible through the Canadian system," he said.
"My sister did her Master's there, my brother went to university there. They got great jobs, they are living very happy lives, my father is happily retired and getting a pension.
"Everybody in the family is grateful and really appreciative of the move that was made. It wasn't easy, but I'm thankful and grateful that I have parents that were willing to give up so much for the three of us."
Raonic held his nerve under pressure to finish with 15 aces and just three double-faults in his winning effort which lasted just over two hours. He said it probably the first time he had won after losing the first set and going down a break in the final set of a match.
Raonic, the 10th seed, will next take on Ukraine's Alexandr Dolgopolov, who defeated Italian 13th-seed Fabio Fognini 6-2, 6-4 after taking out No. 1 Rafael Nadal in the third round at the Tennis Garden.
"For both of us it's about keeping one another out of rhythm," Raonic said. "For me, it's about keeping the points shorter. For him, it's about throwing stuff you wouldn't expect.
"The most important thing is obviously my serve. And the beauty of that is nobody can affect me. The ball is in my hand, and I serve it up and I toss it up when I want to."
Raonic earned his best showing at the first Masters 1000 event of the season by beating Murray after losing in the fourth round a year ago to Jo-Wilfried Tsonga.
Raonic, ranked 11th in the world, was grateful for his serving during the match in which he notched 42 winners.
Raonic showed no signs of the ankle injury which he suffered at the Australian Open two months ago as he played his first event since that problem arose.
The Canadian earned his last victory over a top 10 player when he beat Tomas Berdych in the Bangkok final last September.
"I'm just happy with the way things are progressing," he said. "I focused a lot more this event on my attitude and approach during the matches rather than what I'm necessarily playing and just sort of being very hard on myself on that aspect.
"I have been doing well, and it's allowed me to play well."
Raonic lost the opening set on a break in the ninth game from Murray, the world No. 6 who is still not playing at his former level following autumn back surgery. Raonic reversed his fortune in the second set, putting the fifth seed under pressure are winning it with a break in the final game.
Murray went up a break 2-1 in the third but immediately lost it as Raonic got it back on an error.
Raonic then reached 4-2 with a second straight break of the Scot and moved into the quarter-finals three games later as he fired a forehand winner past his frustrated opponent.