Andy Murray draws on his Olympic legacy to brush aside Milos Raonic

Andy Murray gave his best performance since the Olympics (Getty Images)

Now the title has been won, Ivan Lendl can focus on the next challenge for Andy Murray. "He won his club championship," Murray said of his coach's golfing exploits after his own hugely impressive fourth-round victory over Milos Raonic here at the US Open on Monday night. "He won 9 and 7 in the final, so he was fairly happy with himself when he came in before the match. I think that's his golfing done for the next few days, so hopefully his eyes will be on the quarter-finals now."

Murray had good reason to be happy with himself too, after giving his best performance since the Olympics to earn a quarter-final today against Marin Cilic. His 6-4, 6-4, 6-2 victory over the big-serving Raonic, who is regarded as the best player of his age group, was a good example of the confidence that winning Olympic gold has brought to the Scot.

"The important thing is to remember what you have achieved in the game," Murray said. "If you never look at that and just think how tough Raonic is, then you might not play your best. I need to try and remember that I've won some big tournaments. I've won the Olympics and been in the final at three of the four Slams. I've been at the top of the game for a long time now, so I need to remember that when I get into these situations deep in the big events."

As Monday's match wore on, Raonic looked an increasingly desperate man. The world No 16 had tried everything to douse Murray's fire, but still the flames kept coming. When they shook hands at the end and Murray apologised for getting lucky on some points, Raonic told him: "Don't be sorry. It was simply amazing."

Murray looked razor-sharp. He gave Raonic next to nothing – just six unforced errors in the first two sets – and battered him into submission with a stunning array of passing shots.

Raonic has one of the biggest serves in the modern game, but once Murray had got to grips with it, having seen six aces fly past him in the Canadian's first three service games, he underlined his own reputation as one of the best returners in the business. Raonic's total of 14 aces was paltry by his standards.

While Murray forced 12 break points, converting four of them, the world No 4 did not offer a single chance on his own serve. Murray conceded just nine points in his first 10 service games and won 42 out of 48 points when his first serve found the target. "He took me out of the match," Raonic said. "There wasn't much I could do. I tried everything. I tried three different ways. I tried playing back, playing high to him, I tried coming in a lot. Everything really."

Cilic, who reached the quarter-finals with a straightforward victory over Slovakia's Martin Klizan, has lost six of his seven matches against Murray. The world No 13's only victory was in the fourth round here three years ago, when Murray was hampered by a wrist injury. Cilic broke into the world's top 10 two years ago, but the 23-year-old Croat's career has since stalled, although he has won two titles this year, including the Aegon Championships at Queen's Club.

"When I'm playing well, I feel I can match up with anybody," Cilic said. "But I know Andy's really tough for me to play. On certain days he can serve well, defend well. All things can really go in a good direction for him. Sometimes it's tough to find some openings against him."

Murray rarely looks beyond his next challenge, but the thought of what might lie ahead is clearly in the back of his mind. In the semi-finals, Murray or Cilic will play Roger Federer or Tomas Berdych. "If I can get through the next match then I will have a couple of days off before what is the toughest weekend in our calendar – the semis and finals of the US Open," Murray said.