Murray followed up his upset win over Ugo Humbert with a straight-sets victory over the Canadian, reaching the quarter-finals with a 6-3 6-3 success.
The last eight will see Murray face either Lucas Pouille or top seed Hubert Hurkacz, who he lost to in Cincinnati last month.
However, Murray has since played an exceptional five-setter with Stefanos Tsitsipas at the US Open and the former world number one and three-time grand slam champion is feeling increasingly positive about his game.
"This period has been the most tournaments I've played [recently] and my body feels good and I'm starting to gain just a little bit of confidence with each match," Murray said in his on-court interview.
"[I'm] starting to see the points and how I want to play them again, which is great. There have been times in the past year where I've been a little bit confused and not seeing how the points are developing and stuff, which for me was always a strong part of my game and it made me feel quite uncomfortable on the court when I was feeling that way.
"I'm starting to get that back and the results are coming and my tennis is getting better."
The two other last 16 matches saw second seed Pablo Carreno Busta defeat Mikael Ymer 7-5 6-2, while fifth seed Lorenzo Sonego fell victim to a comeback from teenager Holger Rune, who prevailed 6-7 (6-8) 6-4 6-4.
Pouille came from behind to set up his clash with Hurkacz with a three-set win over qualifier Brayden Schnur, and Peter Gojowczyk was victorious in another first-round match.
At the Astana Open, defending champion John Millman came through a marathon match with Jaume Munar to reach the quarter-finals. The Australian took victory 6-4 6-7 (5-7) 7-5 after three hours and nine minutes.
Seventh seed Laslo Djere needed three sets to see off Lorenzo Musetti but eighth seed Ilya Ivashka had little difficulty beating Timofey Skatov in straight sets.
There were also wins for James Duckworth, Kwon Soon-woo, Emil Ruusuvuori and Carlos Taberner.