The six-time Grand Slam champion has never won the Paris Masters in four previous attempts and now faces losing his place atop the rankings should rival Jannik Sinner win the tournament in the French capital.
Returning from three weeks out of official competition due to an ankle issue, Alcaraz claimed the opening set as he displayed his usual combination of fire and flair.
However, much like his ultimately successful run at the French Open this spring, the Spaniard's level dropped off a cliff mid-match.
This time, he was made to pay.
"I'm really disappointed about my level today," Alcaraz told reporters after the loss.
"I had all the ideas clear, all the goals clear but today even in the first set which I won I felt I could do a lot more than I actually did.
"I have to give credit to Cam... He played really well today, a solid match, and I think that was the key."
The mercurial Norrie, who drew his fair share of admiring gasps from the 17,500-capacity centre court at the La Defense Arena, capitalised on his opponent's errors by breaking him twice at crucial times in the second and third sets.
The 30-year-old said the win was "maybe the number one" of his career.
"I've been working really hard this year so it's nice to get a win like this to make it worth it," added the former world number eight.