Draper reached his first Masters 1000 quarter-final, one day after defeating Stefanos Tsitsipas in his maiden victory over a top 10 player, when 17th seed Gael Monfils retired hurt in Montreal in the second set with the Brit up 6-2 0-2.
The world number 82, who came through qualifying to reach the main draw, frequently relied on his speed and reach as he claimed a fast first set.
Monfils collapsed not long after securing a break early in the second, prompting Draper to cross the court to help him into a chair as the Frenchman cried out and clutched at his right leg.
The Birmingham product continued his run of upsets with a 7-6 (7) 1-6 7-5 dismantling of American 10th seed Taylor Fritz, one day after he knocked out eighth-ranked Andrey Rublev.
Evans roared “yes” and held his arms aloft after qualifying for the tournament’s quarter-finals for the first time, setting up a match against Tommy Paul of the US.
The ninth-ranked player took just one hour and 12 minutes to defeat the 26-year-old, much to the delight of the roaring Montreal crowd, and set up a quarter-final against Casper Ruud.