The 23-year-old Spaniard fought back to win 6-7 (10/12), 7-5, 6-3 to advance to the last four for the first time.
In scenes reminiscent of his iconic French Open final comeback win over Jannik Sinner last season, in which he saved three championship points, Alcaraz again stunned the crowd in Paris as he snatched another improbable victory from the jaws of defeat.
The devastating loss for world number 12 Fritz also ended his hopes of reaching the ATP Finals.
Alcaraz's 20-year-old compatriot, Rafael Jodar, will make his debut appearance at the season-ending tournament, capping off a breathtaking first season after only turning professional last December.
Despite only having played one match en route to the quarter-finals, Alcaraz showed no signs of rustiness early on as he seized his first break opportunity in the fifth game of the opening set, whipping a forehand passing shot around the stranded Fritz.
The Spaniard found himself in a battle to hold serve at 4-3, but staved off three break points to ensure his advantage remained intact.
He was not so lucky two games later, however, as Fritz pounced on another shaky service game to break to love and level the frame at 5-5.
In the tie-break full of thrills and spills, both players had set points come and go before Alcaraz dumped a forehand wide to cede the opener to the Californian.
After recovering from 0-40 to hold early in the second set, Alcaraz pointed to his ear and held his fist aloft in a bid to get the Parisian crowd going - the first but not last call-back to his five-set Roland Garros epic.
But, despite this, he continued to struggle to make any significant inroads on the 196cm Fritz's serve.
Indeed, it was the world number 12 who produced the first break of the set in the seventh game to close in on the win.
Alcaraz staved off a match point and then secured a hold that kept his campaign alive with a sensational backhand slice from well wide of his own tramlines.
A fine passing shot saved a second match point in the next game before Alcaraz further delighted the crowd by unexpectedly wiping out the break.
He then completed the Houdini act by breaking Fritz again to take the meeting to a decider.
The rampant Murcian now had a chokehold on the match and got his nose in front 3-1 in the third set when he forced Fritz to push a volley wide.
Alcaraz still had break points to stave off in a match that always threatened another twist but as it rumbled towards its conclusion he brought up two match points on his own serve, sealing the first with a powerful forehand that Fritz could only get a frame on.