Auger-Aliassime won just 50 per cent of points behind his first serve as Korda claimed an impressive 6-2 6-2 success over the Canadian in one hour and 29 minutes.
In the semi-finals Korda will take on fellow American Frances Tiafoe, who edged out Alejandro Davidovich Fokina 7-6 (7-5) 5-7 7-5 in a tight encounter.
The other last-four clash will see Albert Ramos Vinolas take on Sebastian Baez.
Ramos Vinolas bested Fernando Verdasco 6-2 6-2 to set up his meeting with Baez after the Argentinean rallied from a set down to defeat Richard Gasquet 3-6 6-1 6-4.
At the BMW Open, No.2 seed Ruud fell to Botic van de Zandschulp in the quarter-finals.
The Dutchman won their only previous encounter en route to the last eight at last year's US Open and he triumphed 7-5 6-1 in Munich.
"Maybe the score is easier than it really was," Van de Zandschulp said. "The first set [was] really tight, I think. A great battle in the first one. I had some opportunities to break him in the beginning and didn't take them. Gladly [at] five-all I made the break and held the serve at 6-5.
"[The] second set was a little bit easier, but I think I played really well today."
Next up for Van de Zandschulp is Miomir Kecmanovic, who defeated Nikoloz Basilashvili 7-6 (7-5) 6-2. Holger Rune will continue his impressive run against Oscar Otte in the other semi-final after they overcame Emil Ruusuvuori and Alejandro Tabilo respectively.