The 20-year-old missed last year's event with an abdominal injury and his shaky late-season 2023 form continued on Monday with a 6-7 (3-7) 6-3 6-4 loss in his opening round-robin match.
The loss was a third in a row for Alcaraz, who was beaten by Grigor Dimitrov in the fourth round of the Shanghai Masters before a shock defeat to Roman Safiullin in his first match at the Paris Masters.
Later in the red group, Daniil Medvedev began his campaign with a 92-minute 6-4 6-2 win over fellow Russian Andrey Rublev.
After losing third-set tiebreaks in each of his ATP Finals matches last season, Medvedev extended his lead for most tour-level wins (65) and most hard-court wins (48) this season and provided the perfect start in his bid to equal Novak Djokovic and Alcaraz on six tour-level titles on the year.
Russia's Daniil Medvedev swept past compatriot Andrey Rublev in their ATP Finals opener in Turin.
Zverev, a two-time former champion at the event, has surged back into form over the second half of the season following the ankle injury at the French Open last year that ruled him out for seven months.
The German overcame a scare late in the third set when he was chasing down a forehand from Alcaraz, lost his grip, slipped and fell to the court clutching his left ankle. But Zverev quickly shook it off and held in that game for a 4-2 lead.
"I didn't twist my ankle. I just kind of slipped. And kind of maybe pinched my Achilles, my capsule a little bit," Zverev said.
"Hopefully it's nothing too major and I can continue playing."
Zverev has had off-court issues recently after a German court issued a penalty order against him after allegations that he caused bodily harm to a woman. Zverev has disputed the allegations and is contesting the penalty order.
Carlos Alcaraz suffered a third consecutive loss when he was beaten by Alexander Zverev in Italy.
Alcaraz, who said the surface was the fastest he had played on all year, can still hope to advance from the round-robin format, with the top-two finishers in each four-man group reaching the semi-finals.
"I had a few break points that I couldn't take, and I think that was the key of the match," the Spaniard said.
On their own debut Australian duo Rinky Hijikata and Jason Kubler were beaten 6-2 6-4 by Anglo-Dutch No.2 seeds Neal Skupski and Wesley Koolhof, the Wimbledon champions.
Australia's No.1 doubles player, Matthew Ebden, and his Indian partner Rohan Bopanna, were defeated as well, by Anglo-American pair Joe Salisbury and Rajeev Ram, 6-3 6-4.
The action on day two was preceded by the familiar sight of Djokovic collecting a trophy, this time for being the year-end No.1 for a record-extending eighth time.
Novak Djokovic kisses the trophy as ATP 2023 world No.1, which he collected at the ATP Finals.
Djokovic's Monday morning defeat of Holger Rune sealed his No.1 spot and in the afternoon he returned to the Turin court to be presented with the trophy.
"Finishing the year as No.1 in the world is a dream of every tennis player," Djokovic said.
"It's one of the most difficult things to do in our sport. Winning grand slams and being No.1 in the world are probably the pinnacles."
Alcaraz took the honour last year, but Djokovic bounced back winning three of the four majors and finishing runner-up to Alcaraz at Wimbledon.
With PA.
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