Murray, twice a winner at the Canadian tournament, survived a second-set lapse in concentration to beat Marcel Granollers 6-3 7-6(2).
The second seed had enjoyed a bye into the second round along with the rest of the top nine. He initially displayed few ill-effects of his month off the court in making a confident start to the match.
Murray broke in the third and fifth games of the opening set as he raced out to a 4-1 lead in next-to-no-time before Granollers got one of the breaks back after a double fault and a forehand error from Murray.
The Brit prevented Granollers from causing any more trouble in the opening stanza though, wrapping things up at the first attempt after 48 minutes when the Spaniard went wide with a cross-court backhand.
The early stages of the second set, however, were a completely different story.
This time it was Granollers who was the first to break, grabbing the lead in the fourth game when Murray completely mistimed a forehand and sent the ball far away from the court.
Granollers even enjoyed a set point to level the match in the ninth game, but could only net his forehand after some heavy hitting from Murray, and the Brit went on to break back with a forehand winner.
From there Murray quickly regained his concentration, easily forcing the tie-break before racing through seven straight points to win the breaker 7-2 with a huge forehand return that Granollers could only net in reply.
"It was tricky, it is extremely windy here," Murray said in a courtside interview. "I didn't feel that I had my timing and got pushed behind the baseline."
Next up for Murray will be a third-round clash against Ernests Gulbis, the Latvian coming through a tough three-setter 6-3 1-6 6-1 against in-form Italian Fabio Fognini.
Rafael Nadal was more impressive in his first singles match since a shock defeat at Wimbledon as he overcame Canadian Jesse Levine 6-2 6-0.
Canadian wildcard Vasek Pospisil proved his upset of world number 20 John Isner was no fluke as he stormed to a 6-2 6-4 victory over Czech Radek Stepanek.
Pospisil, ranked 71st in the world but playing well above that lowly standing, will now face sixth seed Tomas Berdych who wobbled at times in his match against Alexandr Dolgopolov but emerged a straight sets winner.
German Tommy Haas, however, lasted just 19 minutes before he retired trailing 5-0 to Australian qualifier Marinko Matosevic.
Frenchman Bernard Paire, who overcame Swiss Stanislas Wawrinka, awaits Matosevic in the last 16.
Montreal Masters results
Alex Bogomolov Jr (Russia) beat 3-David Ferrer (Spain) 6-2 6-4
Nikolay Davydenko (Russia) beat Pablo Andujar (Spain) 6-1 4-6 6-3
11-Milos Raonic (Canada) beat Mikhail Youzhny (Russia) 6-4 6-4
15-Jerzy Janowicz (Poland) beat Frank Dancevic (Canada) 7-6(5) 3-6 6-4
Denis Istomin (Uzbekistan) beat Filip Peliwo (Canada) 6-3 3-6 6-3
4-Rafa Nadal (Spain) beat Jesse Levine (Canada) 6-2 6-0
Marinko Matosevic (Australia) beat 10-Tommy Haas (Germany) 5-0 (Haas retired)
5-Tomas Berdych (Czech Republic) beat Alexandr Dolgopolov (Ukraine) 6-3 6-4
Benoit Paire (France) beat 8-Stanislas Wawrinka (Switzerland) 6-2 7-6(2)
2-Andy Murray (Britain) beat Marcel Granollers (Spain) 6-4 7-6(2)
Ernests Gulbis (Latvia) beat 13-Fabio Fognini (Italy) 6-3 1-6 6-1
Vasek Pospisil (Canada) beat Radek Stepanek (Czech Republic) 6-2 6-4