The second-seeded Murray, a two-time Rogers Cup champion, won his 13th straight match, including his victories at London and Wimbledon, where the Scot became the first male British champion in 77 years.
"I was pretty nervous beforehand -- that was a good sign," Murray said. "I'm pretty ready to move forward and not think too much about Wimbledon and concentrate on the U.S. Open.
"I think in some ways, it's nice. I'll probably never feel that same pressure again. That's why I was nervous today. That's why I'm really happy. It wasn't my best tennis, but the nerves were there and that's a good sign."
Murray will face Latvia's Ernests Gulbis, a 6-3, 1-6, 6-1 winner over Italy's Fabio Fognini.
Rafael Nadal also opened with a victory, routing Canada's Jesse Levine 6-2, 6-0. Also a two-time Rogers Cup winner, the fourth-seeded Spanish star was playing for the first time since a first-round loss at Wimbledon.
"Pleased about the victory, first thing," Nadal said. "After seven weeks without playing a match, starting in a very tough tournament on a fast court, to be through to the third round is good."
Also, fifth-seeded Tomas Berdych of the Czech Republic beat Ukraine's Alexandr Dolgopolov 6-3, 6-4; France's Benoit Paire topped eighth-seeded Stanislas Wawrinka of Switzerland 6-2, 7-6 (2); and Marinko Matosevic had a 5-0 lead when 10th-seeded Tommy Haas of Germany retired. Canada's Milos Raonic, seeded 11th, beat Russia's Mikhail Youzny 6-4, 6-4 in a match briefly interrupted by rain.