British No1 Evans bounced back from an early deficit to defeat American Tommy Paul 1-6 6-3 6-4 in Montreal on Friday night, reaching a Masters 1000 semi-final for only the second time in his career.
However, compatriot Draper will not be his next opponent after being beaten 7-6 6-1 by Spaniard Pablo Carreno Busta.
“You wonder if it’s going to happen, if you are going to get into the match, and I got in,” said Evans.
“When I got ahead I really took it to Tommy and that’s been sort of my way throughout this week so far, and I went about it in a good way, I was fired up and I thought it was a good battle between me and Tommy.”
Carreno Busta, 31, became the only player in Montreal to avoid dropping a set as he knocked out Draper and booked his spot against Evans.
The 20-year-old scrapped hard but Carreno Busta dominated throughout to win 7-6 (4) 6-1, with his younger opponent left to appreciate a week in which he reached his first Masters quarter-final and took down world No5 Stefanos Tsitsipas.
The other semi-final will be contested between Hubert Hurkacz and Casper Ruud, after the former defeated Nick Kyrgios and the latter sent local favourite Felix Auger-Aliassime home.
Additional reporting by the Press Association.