The Spanish second seed, who won his 27th career title in Tokyo last week, was well below his best in a 7-5 7-6 (7-4) defeat.
As well as his seven-match winning streak, Alcaraz will now presumably lose his moustache, having promised to keep it throughout his stay in the Masters 1000 event as part of a bet with his team.
More significantly he also loses any chance of ending the year as world No.1, a status that in the continued absence of the injured Jannik Sinner will be accorded, for the first time, to Germany's Alexander Zverev.
Zverev, 29, won the French Open and US Open titles this year and also reached the Australian Open semi-finals and the Wimbledon final.
"It's been a fantastic season for me winning in Paris and New York and knowing that I will finish the year on top of the rankings is just a dream come true," Zverev, who will play Alexander Bublik in Shanghai on Tuesday, said.
Alcaraz's conqueror, said of his win, the biggest of his career, "It's a bit about disbelief.
"It's a moment where you don't really realise what's going on. I'm going to have to calm down," added the world No.39 from Belgium.Â
"This has been tough for me, I often have too much respect for these guys. To have this moment is a relief. I feel like I can win against these guys."
Breaking Alcaraz for the second time to take a 6-5 lead in the opening set, Bergs used his fourth set point to serve it out after Alcaraz hit the net.
He broke for a 6-5 lead in the second set but failed to serve out the match with the Spaniard breaking back to force the tiebreaker.
Alcaraz, who won last week's Japan Open, fought back from 4-2 down to level but Bergs then recovered to build two match points. The Belgian only needed one.
Next, Bergs will face Tommy Paul after the American knocked out defending champion Valentin Vacherot 6-4 6-2.
Elsewhere, American Taylor Fritz suffered a dramatic collapse against Stefanos Tsitsipas.
The 11th seed led by a set and had dropped just three points on his first serve until the final game of the second.
But Greek world No. 43 Tsitsipas secured a break to level the match and went on to win 3-6 7-5 6-3.
Fifth-seeded Daniil Medvedev eased past Dalibor Svrcina 6-2 6-3 while fourth seed Felix Auger-Aliassime eliminated Pablo Carreno Busta 6-3 4-6 6-1.
But eighth-seed Arthur Fils was KO'd by unseeded Dutchman Botic van de Zandschulp and 14th-seed Learner Tien by Casper Ruud, seeded 20. Rafael Jodar was the day's other singles winner, the 12th seed beating Jiri Lehecka.
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