Wawrinka is through to the last eight at Roland Garros for the fourth time after ending French hopes of a first men's singles champion in Paris since 1983.
The Swiss goes on to face Croatian seventh seed Marin Cilic for a spot in the semifinals.
Cilic went through when South Africa's Kevin Anderson retired with a thigh injury trailing 6-3, 3-0.
He will take a 2-11 losing record against Wawrinka into his match with the Swiss star.
They were joined in the quarters by Briton Andy Murray, who racked up his 650th career win in beating Karen Khachanov of Russia 6-3, 6-4, 6-4.
The world number one, the runner-up in Paris to Novak Djokovic last year, chose not to discuss the match in the traditional on-court TV interview. Instead, Murray took the microphone to remember the 29 people who died in the recent attacks in London and Manchester.
"Obviously there was terrible tragedy in London and Manchester. Paris has had its problems too in recent years," said Murray.
"I am sure everyone will join me... we share our thoughts and prayers with everyone who has been affected.
"I appreciate everyone still coming out to support the tennis. I am grateful that I can still perform in front of everyone."
Murray will face Japanese eighth seed Kei Nishikori who defeated 33-year-old Fernando Verdasco of Spain 0-6, 6-4, 6-4, 6-0.