The defending champion dispatched the German in straight sets with a 7-6(1) 6-2 6-2 victory at Flushing Meadows.
Following the win, Murray revealed that he was pleased to have overcome the "tricky" 29-year-old with relative ease.
"It was very tough conditions," Murray said on court after his win. "He's a very tricky opponent. He plays strange shots and he takes your time away, it's tough to get into a rhythm. I'm really glad to come through in three sets.
"It cooled down a little bit towards the end but the first and second sets it was very hot. We've been told a thunderstorm is coming so hopefully that will take away some of the humidity."
Murray will face the unseeded Denis Istomin in the fourth round.