Murray dominated Djokovic in the first set and held him off in the second, when Djokovic tried to come back.
"It's not easy. You have to try to be as consistent as much as you can if you want to stay at the top,'' Djokovic said. "You have players like Andy, still young and up and coming. ...
"Now there's a lot of great players, and everybody is working hard to get to the top.''
Murray, who had never beaten the 21-year-old Serb in four career meetings, moved beautifully, chasing down loose balls and making difficult shot after difficult shot.
"It's a big win mentally for me,'' Murray said. "You know, the last three times I played him, I lost pretty badly.''
Djokovic, for his part, committed 36 unforced errors to Murray's 19, with 20 of those coming off his forehand.
"In general, I was not really happy with my performance,'' Djokovic said.
Murray, from England, will play Rafael Nadal. The second-seeded Spaniard knocked off No. 10 seed Richard Gasquet of France 6-7 (12), 6-2, 6-1.
Meanwhile, seventh-seeded James Blake became the latest big-name player to lose at the Rogers Cup when he was routed 6-1, 6-2 by Nicolas Kiefer of Germany. Kiefer, ranked 37th in the world, will play Gilles Simon.
Kiefer and Simon are the unlikely victors in a bracket that featured Roger Federer, Nikolay Davydenko, Andy Roddick and Blake.
"I mean, I didn't even know what's happening,'' said Simon, the 22nd-ranked Frenchman who defeated Croatia's Marin Cilic 3-6, 6-2, 6-3 on Friday. "I'm just so confident, I want to win every match, even if I'm tired. I know I'm playing very good at the moment.''
Kiefer dispatched Blake 6-1, 6-2. He said the win wasn't quite as straight-forward as it looked.
"It wasn't easy,'' he said. "Maybe it looks easy, but I also have to play (at a) very high level.''
Kiefer hasn't won an ATP tournament since 2000, in Hong Kong. But Simon wisely isn't taking anything for granted.
"I just hope that we are going to play a great match with a great fight,'' Simon said. "Even if I died on the court, yeah, I'll just give the maximum tomorrow.''
Simon, ranked 22nd in the world, has already beaten Federer, American qualifier Donald Young and Argentina's Jose Acasuso in the tournament.
The match between Simon and Cilic was far from a classic. The players combined for 104 unforced errors, including 64 by Cilic. The 19-year-old Cilic fired 37 winners, while Simon connected on just 15 - but that's his game. He kept the ball in play and waited for Cilic to make mistakes, which he frequently did.
The match didn't quite capture the imaginations of the center-court fans at the Rexall Centre, who were relatively quiet throughout.
"Let's go Federer,'' jeered one onlooker during the second set.
Second-seeded Rafael Nadal, third seed Novak Djokovic, eighth seed Andy Murray and 10th seed Richard Gasquet were scheduled to play later.
In doubles action, Toronto's Daniel Nestor and Serbian partner Nenad Zimonjic have moved on to the semifinals.
The No. 2 seeds defeated France's Paul-Henri Mathieu and Russia's Mikhail Youzhny 7-6 (4), 6-4.
They'll play seventh seeds Lukas Dlouhy of the Czech Republic and Leander Paes of India.
The 44th-ranked Cilic made a mark in the tournament, defeating the sixth-seeded Roddick, 12th-seeded Spaniard Tommy Robredo and Czech qualifier Lukas Dlouhy in an impressive run to the quarterfinals.
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