Berrettini had appeared to be on course for a dominant victory, and although Monfils fought back to make it tough, the 25-year-old got the job done 6-4 6-4 3-6 3-6 6-2 in a gruelling encounter.
Monfils had an uphill struggle amid a sloppy start, with Berrettini breaking to love in the fifth game as the Frenchman committed two unforced errors and a double fault.
That proved to be the only opportunity Berrettini needed, and he subsequently had few issues seeing out the set from there, though Monfils initially appeared sharper early in the second.
An astonishing fourth game then left Monfils looking dejected as Berrettini somehow survived 10 deuces to hold serve after almost 20 minutes – the 25 points played here were almost half the first-set total (55).
Berrettini sensed the mood and went for the kill, losing just two points on serve before going on to close out the set to love.
A reaction did come, however. Monfils finally got his first break of serve as Berrettini's first double fault gifted him a lifeline, the 35-year-old then easing through the rest of the third set.
He kept that up in the fourth as well, with two huge forehand winners helping Monfils go a break up to take charge before ultimately levelling the match, but Berrettini had too much in the decider as he broke in the first game.
Berrettini raced into a 4-0 lead and, although Monfils did pull a couple of games back, the Italian was out of sight and clinched a deserved victory that saw him grab a slice of history.