The British no1 overturned a two-set deficit and won a final-set tie-break to triumph 4-6, 3-6, 6-3, 6-4, 7-6 in a thrilling five-set clash that lasted for four hours on Court 17 at Flushing Meadows on Friday.
Evans is the first Brit to reach the fourth round in New York since Andy Murray and Kyle Edmund both did so in 2016.
The only time the world no27 had previously achieved that feat was at the Australian Open in 2017, when he beat the likes of Marin Cilic and Bernard Tomic before losing to Jo-Wilfried Tsonga.
Evans will face a huge challenge in the round of 16 on Sunday in the form of two-time Grand Slam finalist and 2019 runner-up Daniil Medvedev, with the second seed having eased to a straight sets victory over Spain’s Pablo Andujar.
“I didn’t think I did a bad job really in the first two sets,” Evans - who lost to Sebastian Korda in the third round at Wimbledon in July - told Amazon Prime Video.
“It was very obvious how he was playing me. I think he dropped a little bit. I still had chances in the first two. In the fifth he started to go back that way, serving a lot better. I played a good tie-break. It was tough. I’m looking forward to relaxing.
“Coming back from Wimbledon where I was poor in the third round, it was difficult. My focus was really third round here once I got there was to put in a good performance today. I could have lost that match pretty easily. I had a great effort regardless so I’m proud of what I’ve done.”