The defending champion dropped a set but still lodged a 7-5 6-1 3-6 6-1 victory over the Argentine slugger, finishing strongly in a typically electrifying atmosphere at a packed Louis Armstrong Stadium.
Britain's number three seed has become such a drawcard at Flushing Meadows that the queue for his clash stretched hundreds of metres back to Arthur Ashe Stadium.
Mayer's aggression paid dividends in the third set before Murray knuckled down in a blistering fourth set to close out the win in two hours and 41 minutes.
"I was a bit frustrated at points in the match because I was doing quite a lot of the running," Murray said.
"I wasn't getting much depth on my returns. I served a low percentage today. You don't feel like you're dictating the match. It can be frustrating, but I finished the match well.
"I played well when I needed to. That's a good sign. I want to keep improving as the tournament goes on. You don't want to play your best right at the beginning."
Murray's first serve was poor. He landed a mere 57 per cent of his first deliveries but his renowned fitness and defensive capabilities kept Mayer at bay in an arena that descended into organised chaos at times.
Spectators were late to their seats and called out between points on a court that has been home to numerous close struggles for Murray in recent years.
"It's a court I haven't played my best tennis on, that's for sure," he said. "I've had some tough matches there in the past, and today was the same.
"But I'm happy to play on any court. It doesn't really make a huge, huge difference. We got a great crowd out there.
"It was a really good atmosphere from pretty much the first point through to the last. Whether or not I play well on that court, it's always a really good atmosphere."
Frenetic crowd activity is a hallmark of the U.S. Open and Murray said he would never complain about the noise of the fans because he revelled in the different atmospheres at the four major championships.
"At this tournament, on all of the big courts, it's very different to Wimbledon, for example," he said.
"It's something you need to enjoy about the tournament. It's quite loud. There's always noise during the points. There's a constant kind of murmur you hear whereas at Wimbledon, it's pretty much silence.
"It's a different atmosphere, and one that I enjoyed when I came here the first time as a kid, playing the juniors.
"You just have to get used to it each time you come back. All of the slams have very, very different atmospheres."
Impatient while waiting until late in the evening to play his first round match on Wednesday, Murray said scheduling problems were now the least of his concerns.
His next match will be against another Mayer, Germany's unconventional Florian. They have met twice, on European clay, and Murray has prevailed on both occasions.
"It was quite a wait to play the first match," Murray said. "By the time I got on (court) Wednesday night, I literally wanted to play. I wasn't thinking about anything else. Maybe in that way, it helped me a little bit.
"But I'm in the tournament now. I play every other day. I'll stick to the same routines pretty much until the end of the tournament."
(Editing by Nick Mulvenney)
