Having suffered a third consecutive defeat to Raonic at the Australian Open last month, Wawrinka beat the big-serving Canadian 6-4 7-6 (7-4) on Wednesday.
The three-time grand slam champion's previous win over Raonic came en route to winning this tournament four years ago and he claimed the only break of the match in the first set before edging a second-set tie-break.
There were only three break-point opportunities in a tight contest as wildcard Wawrinka booked a meeting with Denis Shapovalov in the last eight.
Shapovalov came out on top against Tomas Berdych in a battle between youth and experience, winning 6-4 6-3.
The teenager struck 33 winners to oust the former world number four, who reached the semi-finals of the Open Sud de France last week after starting his season with a run to the final of the Qatar Open following a long absence due to a back injury.
Australian Open semi-finalist Tsitsipas fell at the first hurdle, Damir Dzumhur defeating the third seed 6-4 1-6 7-5.
Gael Monfils reached the quarter-finals by rallying to beat Andreas Seppi 4-6 6-1 6-3, while Daniil Medvedev, Jo-Wilfried Tsonga and Marton Fucsovics all made it through to round two.