Labeling it "the biggest win of my career," Norrie's triumph marked his first-ever victory over a world number one.
The Brit, who was forced out of last year's Olympic Games and US Open with a forearm injury, showed immense grit and composure to turn the match around.
"Coming back from injury, I've tried to just enjoy my tennis. To beat the most confident player in the world right now feels incredible," he said after the match.
After losing the opening set, Norrie struck early in the second to seize the game and force a decider.
The world number 31 produced a stunning backhand pass to break Alcaraz in the final set and saved two break points to close out the match.
Reflecting on his composure, he revealed, "I went for a walk with my coach this morning, talking about how to handle serving for the match. I told myself I deserved to be in that moment, and it worked."
For Alcaraz, it was a frustrating return to action after an ankle injury sidelined him since September.
The Spaniard hit 54 unforced errors and admitted his level was well below par. "Even in the first set, I knew I could do more," Alcaraz said. "But credit to Cam, he played a really solid match."
Norrie will next face the winner between French wildcards and cousins Valentin Vacherot and Arthur Rinderknech, as he looks to build on the biggest result of his career.