World No.5 Tsitsipas, who was a semi-finalist at last month's Australian Open, defeated No.7 seed Auger-Aliassime 7-5 4-6 6-3 in Acapulco.
In a tight contest, back-to-back double faults from Canadian sensation Auger-Aliassime in the eighth game of the third set proved costly as Tsitsipas broke after the pair had held serve throughout the last.
"It got really tight," Tsitsipas said. "I got a bit lucky with the double faults towards the end of the match.
"I was just persistent. Towards the end I had zoned in 100 per cent. Both of us brought an amazing energy out on the court. Felix is someone I've played a lot and I have huge respect for him."
Greek star Tsitsipas will next play emerging Italian teenager Lorenzo Musetti for a spot in the ATP 500 tournament decider.
Qualifier Musetti, who upstaged No.3 seed Diego Schwartzman in the first round, stunned No.5 seed Grigor Dimitrov 6-4 7-6 (7-3) in the final match of the day.
The 19-year-old Musetti will now contest his maiden ATP 500-level semi-final as he prepares to enter the top 100 on the men's tour after just his fourth main-draw appearance.
German Alexander Zverev – the No,2 seed – progressed to the semi-finals with a walkover after No,8 seed Casper Ruud withdrew because of a wrist injury sustained in practice.
Zverev will play countryman Dominik Koepfer in the final four after he defeated Cameron Norrie 7-5 6-4, maintaining his run of not dropping a set all tournament.