Hit with cramp during his first-round win, Murray double-faulted to send the match to a fourth set but then swiftly took care of business in a 6-1 7-5 4-6 6-2 win.
"He played some good stuff at the end of the second set and all through the third," eighth seed Murray said. "I just tried to stay solid in the fourth set and thankfully it paid off.
"I feel better than I did in the first match, obviously. I made sure I did everything properly. I ate properly, drank properly and I felt a lot better today."
Murray had more trouble with the swirling wind around the Armstrong Stadium court and the cramped area beyond the baseline, as opposed to the centre court at Arthur Ashe Stadium.
"The wind swirls a lot on that (Armstrong) court. It can be windy on Ashe, but normally it goes in one direction," said Murray, the 2012 U.S. Open winner and 2013 Wimbledon champion, who has often struggled at the Open's second featured court.
"Also it's a very tight, tight court as well. There's not much runback compared with Ashe. I don't know, outside the lines there's not that much space."
Murray became annoyed at the lack of room at one point when he was headed toward a camera while chasing down a ball.
"I almost ran with my knee straight into the camera at the back of the court," the Scotsman said.
"If I was a spectator, and a player had to stop because he got hit by a camera that was too close to the back of the court, then I would be annoyed if I was watching that. You certainly wouldn't get that an Ashe because there's much bigger runback."
Next up for Murray will be ninth seed Jo-Wilfried Tsonga of France, who beat Spain's Pablo Carreno Busta 6-4 6-4 6-4.
Tsonga beat Murray in three tight sets in the quarter-finals in Toronto earlier this month on his way to winning the title.
"It will be a tough match. We played each other a lot of times," said Murray. "He's obviously playing well right now. He had a great week in Canada. He's played some good tennis so far here. Obviously it will be a tough match.
Despite the Toronto loss, Murray has won nine of 11 matches against the Frenchman.
"I've had a lot of close matches with him," Murray said. "But I've won a lot against him, as well. I would say my game matches up well with his."
(Editing by Peter Rutherford)
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