Wawrinka bickered heatedly with the 12th seed during a change of ends after the first set before putting his aggression to better use, wrapping up the one-sided match in two hours and 15 minutes on a sun-bathed Rod Laver Arena.
Fourth seed Wawrinka will battle either compatriot Roger Federer or German giant-killer Mischa Zverev, who face off in the late quarter-final, for a place in the final.
Wawrinka, the 2014 champion, put in his most complete performance of the tournament against Tsonga, sending 41 sweetly struck winners whistling past the out-of-sorts Frenchman, a former finalist but a shadow of his usual energetic self.
Tsonga put up some stout resistance early in the match but that crumbled in the first set tiebreak when he elected not to play at a blazing backhand pass.
It landed flush in the corner, giving Wawrinka four set points and Tsonga folded on the first of them.
