It was a third career title but a first on hard court for the 26-year-old Argentine claycourt specialist, who dropped to the ground in jubilation after completing the win in an hour and 43 minutes when Fritz sent a forehand wide.
After a trade of service breaks in the opening set, Schwartzman had to dig deep at 6-5 40-0 down but some big serves and forehands got him out of trouble and he forced a tiebreak.
ATP Rome doubles
Murray to play Italian Open doubles with Broady
Fritz's serve was to let him down at crucial moments in the match and a couple of double faults in the tiebreak helped hand the opening set to Schwartzman.
The 21-year-old American received a point penalty to go down 3-1 in the second set but he fought back to lead 4-2 before Schwartzman regrouped to break his opponent again for a 5-3 lead and served out for victory.
In-form Norrie battles past Carballes Baena in straight sets
'I'll be ready' - What to expect from Serena at the Italian Open