Spaniards flocked to Valencia to see 19-year-old Alcaraz in his first match since he won the US Open last weekend.
Instead, they witnessed their new idol succumb to a superb Auger-Aliassime, who endured the partisan crowd and tilted the match his way after Alcaraz dug deep to claim the first-set tiebreaker.
"Felix is a beast. Physically and mentally, Felix is one of the best in the world," Alcaraz said. "I was right there, fighting, but I wasn't able to show my top form. It got away from me in the details.
"I didn't come in very good physical condition," he added. "It was a very tough day, but I have to say congratulations to him because he played an unbelievable game."
As the pavilion roared for Alcaraz, Auger-Aliassime coolly responded by surgically placing shot after shot exactly where he wanted. He dominated on his serve with 16 aces and eventually broke Alcaraz late in the second set and twice in the third.
"He is the world No.1 and big credit to him for that, but today I think I was a little bit better in the third set," the 13th-ranked Auger-Aliassime said. "I wasn't going to let my team down with my fighting spirit."
Roberto Bautista gave Spain the first point after he fought back for a 3-6 6-3 6-3 win against Vasek Pospisil, who needed medical treatment to his upper left thigh. The group tie will be decided in doubles.
Bautista helped Spain beat Serbia 3-0 on Wednesday while Alcaraz was resting after jetting home from New York where he won his first grand slam on Sunday after a gruelling run that included three consecutive five-set victories.
In Glasgow, Britain were knocked out of the Davis Cup Finals as Andy Murray and partner Joe Salisbury lost a deciding doubles to Dutch pair Wesley Koolhof and Matwe Middelkoop.
Just as against the United States in their opening tie on Wednesday, Murray and doubles world No.1 Salisbury took to the court with the tie locked at 1-1.
They saved a match point in a nerve-jangling second set but eventually succumbed 7-6 (7-0) 6-7 (8-6) 6-3.
While the Dutch celebrated wildly at sealing their place in the quarter-finals to be played in Malaga next month, Britain were left with their hopes in tatters.
The Dutch pair broke serve to lead 5-3 in the decider and closed it out in nerveless fashion on Koolhof's serve.
Earlier, Dan Evans had given Britain the lead with a comfortable victory over Tallon Griekspoor but Cameron Norrie was overpowered by Botic van de Zandschulp.
Murray and Salisbury fell just short again, as they did on Wednesday when losing in three sets to Jack Sock and Rajeev Ram.
The Netherlands will play the United States on Saturday to decide who wins the group with Britain's match against Kazakhstan now just about salvaging pride.
