Playing under lights on a windy Arthur Ashe Stadium, the British eighth seed cruised past German Matthias Bachinger 6-3 6-3 6-4 on Thursday.
It was far more comfortable than his first-round win over Dutchman Robin Haase on Monday, when Murray suffered from cramps.
The two-time grand slam champion hopes the problems are behind him, and said he had felt in good condition leading into his clash against Bachinger.
"I hope [it's all behind me]," Murray told a news conference.
"I hope I feel better every day now. I felt fine the last couple days. Had no problems, you know, on the Tuesday or Wednesday. I practised well and didn't have any problem. Tonight was fine, too."
Murray is unsure what caused the cramping against Haase, but several players have struggled in the New York heat in the first week.
"It's very difficult to know exactly why that happens," he said.
"Sometimes, you know, you can train as much as you want, drink as much. You know, I could have just missed something with my eating or drinking. That's definitely a possibility.
"Maybe I could have eaten a bit more before the match. Maybe the couple days before in the lead-up. I don't know.
"A few of the players have had some issues the last few days. So I don't know if it was purely down to the conditions or not.
"But I played in hotter, more humid conditions than that and have been fine. So I don't know."
Murray faces Andrey Kuznetsov in the third round after the Russian's surprise five-set win over Spanish 31st seed Fernando Verdasco.
The two have never met, but Murray believes the fast courts at Flushing Meadows will suit the 23-year-old.
"He's had a couple big wins in the slams this year. He beat [David] Ferrer at Wimbledon and obviously today against Verdasco," Murray said.
"I've never played him before. I don't know his game that well, but I've seen him play a little bit. He hits the ball pretty flat. Likes to go for his shots a lot.
"This court's fairly quick, so that will probably help him, as well. But I'll watch a little bit of video tomorrow evening, try to understand his game a bit better."