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.
"Probably this match is going to be one of the most special matches that I ever played, and I'm going to remember this match for a long time," Alcaraz told reporters.
Despite only playing one match en route to the quarter-finals, Alcaraz showed no signs of rust 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's serve started to wobble and Fritz pounced to break to love and level at 5-5.
In a tie-break 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 he continued to struggle to make inroads on Fritz's serve.
Instead, the American produced the first break of the set in the seventh game.
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.
"After that game... I started to enjoy it because I just thought I pulled off great shots, great points, I started to smile, I started to bring the energy from the people to the match," the former world number one said.
A fine passing shot saved a second match point in the next game before Alcaraz wiped out the break and then completed his Houdini act by breaking Fritz again to set up a decider.
The rampant Murcian had a chokehold on the match and went in front 3-1 in the third set when Fritz pushed a volley wide.