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A win on Saturday would also give the 36-year-old American a seventh US Open title, breaking a tie with Chris Evert for the most in the Open era.
Naomi Osaka became the first Japanese woman in 22 years to reach the semifinals of a Grand Slam.
Madison Keys eased into the quarter-finals of the US Open with a 6-1 6-3 victory over Slovakia's Dominika Cibulkova.
Sloane Stephens, Serena Williams, Rafael Nadal and Juan Martin del Potro advanced to the fourth round of the US Open on Friday in contrasting fashion.
World number one Simona Halep turned back American Sloane Stephens 7-6(6), 3-6, 6-4 to win the final in Montreal.
It is time for women to break open the door and change things, says the actor.
Williams, who won the Wimbledon title on her last two visits in 2015 and 2016, is now on an 18-match winning streak at the All England Club.
All you need to know about nerve agent Novichok
The win followed the victory for Wawrinka's girlfriend Donna Vekic, who demolished fourth seed Sloane Stephens, earlier in the day.
US Open champion Stephens tumbled out, as she looked rusty and out-of-sorts in her 6-1, 6-3 defeat by Croatia's Donna Vekic.