Wawrinka earlier defeated US comeback king Donald Young 6-4 1-6 6-3 6-4 to book his place in the last eight.
Wawrinka dropped his first set of the tournament but made an eighth quarter-final in his past nine grand slams, denying 68th-ranked Young his first trip to a major quarter-final.
"The set was so quick. I wasn't there mentally," Wawrinka said of his second-set let-down.
"Calmed down a little bit. I began to be more aggressive, started moving my feet better."
Young was the first player since Gilles Muller in 2008 to rally twice from two sets down in a US Open, having been 0-17 in such matches before this week, but the left-hander fell to 3-18 against top-10 opponents.
"He had the crowd. It was a tough match for sure," Wawrinka said. "It was a great atmosphere."
Swiss second seed Roger Federer, a five-times Open champion chasing his first title since 2008, will face American 13th seed John Isner in the night session at Arthur Ashe Stadium.
Federer, 34, is trying to become the oldest US Open champion since Ken Rosewall in 1970 has a 4-1 career edge on Isner and has won 12 consecutive US Open matches over American foes since losing to Andre Agassi in 2001.
The Anderson-Murray epic delayed the start of the final men's last-16 match-up between Czech sixth seed Tomas Berdych and French 12th seed Richard Gasquet.