The five-time Grand Slam champion made it two wins from two in the Jimmy Connors Group with a comeback 6-7(2), 7-5, 6-3 victory over last year's runner-up Fritz in Turin.
He will qualify for the semi-finals if Alex de Minaur beats home hope Lorenzo Musetti in Tuesday's second match.
"I'm really happy that I was able to come back, find my good tennis," Alcaraz said.
"I just tried to make the most of the opportunities that he gave to me. I think we played great tennis, some great points."
Alcaraz, who was replaced by rival Jannik Sinner as world number one following the Paris Masters earlier this month, will finish 2025 at the top of the rankings if he beats Musetti on Thursday.
Sinner has to successfully defend his Finals title, unbeaten, to have any chance of ending the season as number one for a second straight year.
Alcaraz now holds a 5-1 winning record against Fritz, whose only win against the Spaniard came at the Laver Cup in September.
The United States' Fritz will face De Minaur in his last group contest.
Gruelling first set
Fritz swept aside Musetti in his opener on Monday with a dominant serving display.
Alcaraz immediately showed he would put up stronger resistance on return, but Fritz managed to hold in a lengthy first game, hitting three aces and saving two break points.
The Spaniard also had to dig deep to level at 1-1, staving off three break points himself.
He appeared to have made the most of that mistake as Fritz was broken for the first time in the tournament, but Alcaraz could not consolidate the break and dropped serve too.
Both players' serves continued to be tested, with Alcaraz seeing off two more break points in the eighth game as the first set eventually went to a tie-break.
But Fritz powered through the breaker, sealing a one-set lead after 70 minutes with his sixth ace.
Some brutal hitting with his forehand brought up the first break point of the second set for Fritz in the fifth game, but Alcaraz came out on top in a dramatic rally to save it.
Alcaraz saw off a second break point with an ace and finally got out of the draining, 21-minute service game when Fritz fired long, celebrating as if he had won the match.
Fritz fought through a difficult game himself to make it 4-all after Alcaraz netted a return on break point, as the second set edged towards another tie-break.
But the American buckled under the pressure in the 12th game, as two wild unforced errors helped bring up three set points for Alcaraz.
The 22-year-old took the second opportunity, with a rasping passing shot, forcing a deciding set.
Fritz managed to stay on serve early in the third set, but the momentum of the match had shifted, and Alcaraz grabbed the crucial break in the sixth game.
Sixth seed Fritz showed great resolve to save three match points in game eight, but Alcaraz successfully served it out to love, sealing the win as Fritz blasted a backhand wide.
