The third seed produced one of his best performances of the season to completely nullify the threat of big-serving Milos Raonic in the fourth round at Flushing Meadows on Monday.
Since the US Open in 2010, Murray has managed one quarter-final, four semi-finals and two finals at the sport's biggest tournaments as well as winning an Olympic gold medal.
The Scot will be a big favourite to beat Cilic, whose only win in seven previous meetings with Murray came here three years ago, to set up a probable semi-final clash with Roger Federer.
Murray said: "I've played well in the slams and most of the big events over the last couple of years. That's what I want to be doing at this stage of my career.
"I said it didn't matter how many Masters Series or whatever I won or how well I played in them, I just always got asked about my performances in the slams. So it seemed like that was the only thing anyone was bothered about.
"I'm glad my consistency has been better in them. I have played my best tennis in the slams, and I hope it can continue."