The Spanish world number two recovered from losing the opening set and saved two match points before completing a memorable victory after two hours and 43 minutes at the Plenitude Arena.
Fritz, the 11th seed, appeared close to securing a place in the last four after taking the first set and establishing a 5-3 advantage in the second.
However, Alcaraz showed his fighting qualities, using the energy of the Paris crowd to turn the contest around.
Fritz takes opening set in dramatic tie-break
Alcaraz made an encouraging start, breaking Fritz to move 3-2 ahead before serving for the opening set at 5-4.
The American responded by breaking back to level the contest, forcing a tie-break after a closely fought opening set.
Both players had opportunities to take the set, but Fritz eventually converted his third set point to win the tie-break 12-10.
The result put the American in a strong position as he continued to threaten Alcaraz with his powerful groundstrokes and aggressive baseline play.
Alcaraz saves two match points to force decider
Fritz carried his momentum into the second set, breaking Alcaraz to take a 4-3 lead before extending his advantage to 5-3.
The American then moved within a point of victory when Alcaraz was serving at 3-5, but the Spaniard produced a brilliant response to save the first match point.
Fritz had another opportunity to close out the contest while serving at 5-4, but Alcaraz produced a spectacular passing shot to deny him again.
The Spaniard broke back, regained control and won four consecutive games to take the second set 7-5.
Spaniard completes stunning comeback
Alcaraz carried his renewed confidence into the deciding set, winning four of the first five games to establish a commanding advantage.
Fritz attempted to fight back, but the Spaniard maintained his composure and eventually secured a 6-3 victory to complete the comeback.
Speaking after the match, Alcaraz praised the Paris crowd for helping him overcome the difficult moments.
He said the support reminded him of his dramatic comeback against Jannik Sinner in the 2025 French Open final, when he saved three championship points before winning the title.
Alcaraz described the encounter as one of the most special matches of his career.
Fritz misses ATP Finals qualification
The defeat ended Fritz's hopes of qualifying for the 2026 ATP Finals in Turin.
The American needed to reach the Paris Masters semi-finals to overtake Spain's Rafael Jódar in the race for the final qualification position.
Fritz's elimination therefore confirmed Jódar's place at the season-ending tournament.
Alcaraz, who had already qualified, will continue his campaign against Norway's Casper Ruud in Saturday's semi-final.
Ruud booked his place in the last four after defeating Portugal's Nuno Borges 7-6(5), 6-4.