German world number three Alexander Zverev is also through to the last four in Vienna after Dutchman Tallon Greekpoor withdrew from their quarter-final.
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.
Norwegian Casper Ruud decided he could not continue after losing a first-set tiebreak to Spaniard Alejandro Davidovich Fokina, and Canadian Felix Auger-Aliassime retired after Spaniard Jaume Munar won the first set 6-3.
Canadian Denis Shapovalov shook hands with Joao Fonseca after falling behind 3-6, 6-3, 4-1 against the Brazilian.
In the only match played in Basel, Frenchman Ugo Humbert defeated American Reilly Opelka 7-6 (7-0) 6-4.
Several high-profile players have seen their seasons end prematurely in recent weeks.
After a serious injury to Holger Rune, British number one Jack Draper earlier in October called for the tennis calendar to be adjusted if players want to “achieve some kind of longevity”.
Former women’s world number one Iga Swiatek complained in September that the season is “too long and too intense” amid a series of injuries to players at the China Open.
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