Wawrinka will play the winner of the night quarterfinal between Roger Federer and Mischa Zverev.
It was Wawrinka's fourth win in a row over Tsonga and the first meeting between the pair at a Grand Slam other than the French Open, where they had met three times, with Wawrinka holding a 2-1 edge.
It was also the pair's first meeting on a hardcourt in nearly 10 years — at Metz, France in 2007, when Tsonga won.