Pushed off Arthur Ashe Stadium court to Louis Armstrong because of unsettled weather, Wawrinka did his part to wrap up action quickly brushing past the overwhelmed 15th seed in just one hour, 47 minutes.
"We wanted to play on Ashe but I think it was the better thing to do if we wanted to play all matches today," said French Open champion Wawrinka. "It was tough with the rain this afternoon.
"At the end of the day, for me I don't really mind where I'm playing. I'm trying to be focused on the match, and I was ready for both."
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Anderson lacked the energy he displayed in a fourth-round upset of third seed Andy Murray, allowing the Swiss to dictate play for large stretches of the match.
The South African, who relies heavily on his serve, managed just nine aces and one break chance the entire match, which he could not convert.
"Obviously it was a big moment for me but I felt I did a good job of resetting myself and getting ready for this next match," said Anderson. "But obviously wasn't meant to be.
"Stan didn't make it easy. He was swinging out, and I was just a step slow. I needed to be on top of my game."
Wawrinka will now meet compatriot Roger Federer in the semi-finals, the pair have clashed 19 times during their careers with Federer holding a sizeable 16-3 edge.
"I think the past three years, for sure, I get closer to him (Federer)," said Wawrinka.
"My level improved a lot. I'm playing better tennis.
"I will for sure need to play my best tennis. He's playing really well so far.
"He loves to play. He knows how to play. He had some amazing match. It's going to be a big challenge. I think I'm ready."
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