The Olympic champion had played one match at the Rogers Cup in Toronto last week before withdrawing as a precaution to protect his knee.
His first match back in action looked like a tricky tie against an American on a home court ranked inside the world's top 30, but after sharing the four opening games Murray pulled away in style.
Querrey could make little impression on the Murray serve, blocking the ball back into play rather than attacking it.
On his own serve, the American was undone by the world number four's irresistible defensive work. On several occasions Murray kept smashes and vicious shots in play, forcing errors which turned games his way.
He broke Querrey on three straight service games, wrapping up the first set in just over half an hour and building a break advantage in the second in the process.
By the time the world number 29 arrested the slump, it was too late.
He earned his first two break points in Murray's penultimate service game, but a couple of commanding forehands from the Scot snuffed out the chance.
And Murray held with confidence to close out the game and set up a last-16 clash with France's Jeremy Chardy, who had earlier overcome Denis Istomin in straight sets.
Murray said Querrey's recent run of good form had made him raise his game.
"He's had some good wins, so I was expecting a tough match. I think that helped me," said the Scotsman.
"I was very sharp right at the beginning of the match. I needed to be, and it was a good start to the tournament," he said.
The main positive for Murray was that he had no discomfort with his knee.
"It felt fine. I moved well today. It was still giving me a little bit of trouble in practice for a couple of days before the tournament, but it felt much, much better on the court today. I moved well, so I'm hoping it won't be a problem," he said.