The Canadian is targeting his first singles title on the ATP Tour and is making good progress in Rotterdam having booked his place in the semi-final.
Norrie, who was hoping to avenge Andy Murray's defeat to the Canadian, put on a strong display but ultimately fell to a 7-5 7-6 defeat.
The Brit fought back from a break down in the opening set and then opened up an early lead in the second before Auger-Aliassime levelled at 4-4.
Norrie saved two match points in the 12th game to force a tie-break, but Auger-Aliassime moved into a 6-2 lead before taking his fifth chance to wrap up victory.
Auger-Aliassime, who held a match point against Daniil Medvedev in the quarter-finals of the Australian Open, reached the final of this tournament back in 2020 but fell to a straight sets defeat to Gael Monfils.
He will now be looking to end his eight-match losing run in ATP tournament finals as he looks to claim his first piece of major silverware.
Elsewhere, twenty-year-old Czech Jiri Lehecka continued his breakthrough run by beating Italian Lorenzo Musetti 6-3 1-6 7-5 to reach his first ATP Tour semi-final.
There, he will face top seed Stefanos Tsitsipas, who has picked up where he left off at the Australian Open and saw off Australia's Alex De Minaur 6-4 6-4.
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