German world number three Alexander Zverev is also through to the last four in Vienna after Dutchman Tallon Griekspoor withdrew from their quarter-final match.
With that result, Zverev, seeded second in Vienna, joined Alcaraz, Sinner and Novak Djokovic as the first four players to qualify for the season-ending ATP Finals in November.
Zverev will play Italian fourth seed Lorenzo Musetti or Frenchman Corentin Moutet in the other semi-final on Saturday.
Meanwhile, at the Swiss Indoors, three of the four quarter-finals scheduled for Friday ended as walkovers.
Norway’s Casper Ruud decided he could not continue after losing a first-set tie-break against Spain’s Alejandro Davidovich Fokina, and Canada’s Felix Auger-Aliassime retired after Spaniard Jaume Munar won the first set 6-3.
Canadian Denis Shapovalov shook hands with Joao Fonseca after falling 3-6 6-3 4-1 behind against the Brazilian.
In the only match to be completed in Basel, Frenchman Ugo Humbert beat American Reilly Opelka 7-6 (7-0) 6-4.
Several high-profile players have seen their seasons ended prematurely over recent weeks.
Following a serious injury to Holger Rune, British number one Jack Draper called for the tennis calendar to be adapted if players are “to achieve some sort of longevity” earlier in October.
Former women’s world number one Iga Swiatek complained in September that the season is “too long and too intense” amid a string of injuries to players at the China Open.
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