Canada's Raonic struggled throughout against Murray, who eventually ran out a 6-4 6-4 6-2 victor at Flushing Meadows.
After the match, Raonic admitted that no matter what he tried, Murray always came up with an answer.
"Not much I could do. I tried everything," Raonic told a press conference. "I tried three different ways. I tried playing back, playing high to him. I tried coming in a lot. Everything really. He took me out of the match."
Raonic had never reached the last 16 in New York before this year.