The British number one only arrived in Canada on Tuesday but beat Italian Flavio Cipolla 6-1 6-3.
He required treatment on his knee, which lasted just under 90 minutes.
"I was stiff and sore," said Murray. "I had a lot of matches at the Olympics and this was my first match on a hard court in four months."
Roger Federer and Rafael Nadal apulled out of the event but Murray, who was handed a bye in the first round, will now meet 16th seed Milos Raonic for a place in the quarter-finals.
Organisers presented Murray, who won gold in the singles and silver in the mixed doubles with Laura Robson, with a huge chocolate cake celebrating his Olympic medal.
Jo-Wilfried Tsonga, who won silver in the men's doubles event at the Olympics, lost his opening second-round singles match 6-4 7-6 (7-4) to fellow Frenchman Jeremy Chardy.