The tournament is Raonic's first event since a short layoff to undergo minor surgery to correct a pinched nerve in his right foot.
"The tennis I thought was great," said the third-seeded player from Thornhill, Ont. "The only thing I really have to be disappointed with is I wish I would have sort of gutted it out a bit more, tried to play on my terms. I was waiting for him too much and I let him dictate."
The seventh-seeded Simon surrendered the opening set on a single break of serve at 1-1, but in a 12-minute game at 2-2 in the second set he fought off three break points before breaking for a 4-2 lead.
Neither player earned a break point in the final set until at 5-5, when a netted backhand gave Simon the decisive break. He needed five match points to close it out in 2 hours, 18 minutes.
"I couldn't return any serve in for one set and a half," Simon said. "I had a lot of trouble to win my service game. I was under pressure every time. And then I don't know how it turns, a bit out of nowhere."
Meantime, top-seeded Andy Murray stayed on course for a fourth Queen's title by overcoming Gilles Muller of Luxembourg 3-6, 7-6 (2), 6-4 on Friday to reach the semifinals.
Like in previous matches this week, Murray struggled early against a solid opponent. Muller broke to lead 3-1, and Murray failed to convert two break points in the next game. The second set then went with serve until Murray finally raised his game and was able to dominate the tiebreaker.
He then broke early in the third, which was enough to decide the match.
Simon will next play South Africa's Kevin Anderson, who beat Spain's Guillermo Garcia-Lopez 7-6 (7), 7-5.
Anderson, who saved a match point against Lleyton Hewitt in the first round, hit 18 aces but failed to earn a break point until leading 6-5 in the second set.
There were just two other break points in the match, which Garcia-Lopez failed to convert in the opening game of the second set.