Lasting for one hour and 11 minutes, the first set at Stadio Centrale was simply breathtaking and required a tiebreak.
Perhaps Alcaraz was buoyed after taking the lead or Sinner's head had dropped, but the second set lasted just 34 minutes as the Spaniard took the win.
Alcaraz, who will climb to world number two on Monday, claimed his third title of the season ahead of the French Open.
Sinner tops the world rankings, but his 26-match winning streak was ended in Rome by Alcaraz - also the last man to beat him.
With this victory, Alcaraz has sent a message to the rest of the men's tour before attempting to defend his title at Roland-Garros from next weekend.
A warm-up for Sinner?
Finishing runner-up is still a positive result for Sinner in his first tournament since a three-month ban for testing positive twice last year for traces of clostebol, a contamination doping authorities accepted was accidental.
His progress in Rome also sets up the possibility of another final clash with Alcaraz at Roland-Garros, with the two young stars of men's tennis set to be the two top seeds in Paris.
Sinner was gunning to become the first Italian man to win at the Foro Italico since Adriano Panatta back in 1976, but he failed to make it a hat-trick of triumphs for home players in the Italian capital.
Earlier, Jasmine Paolini became the first woman since Monica Seles in 1990 to win the Rome singles and doubles titles when she and Sara Errani beat Veronika Kudermetova and Elise Mertens 6-4, 7-5.
Paolini secured that brace of victories a day after overcoming Coco Gauff in straight sets, and becoming the first Italian woman to win the Rome singles title since Raffaella Reggi in 1985.