Italian home favourite Berrettini edged a thrilling first set, which clocked in at 75 minutes long, and faced another stern challenge in the second on Wednesday.
At one point trailing 4-2, the world No.16 fought back to set up a tiebreaker that was equally tight, with Carballes Baena fighting back from 4-2 down to force a decider.
With the clock past the three-hour mark, Spaniard Carballes Baena capped off a remarkable comeback in the third set to send Berrettini tumbling out of the tournament, coming back from a break down once again.
“I’m very happy, it’s a very good win for me, the best of my career,” Carballes Baena said.
The world No.80 will face Mikael Ymer in the quarter-finals of the indoor, hardcourt tournament after the Swedish qualifier eliminated fifth-seeded Russian Aslan Karatsev 6-1 6-7 (6-8) 6-1.
Fourth seed Maxime Cressy and sixth-seeded Jenson Brooksby are also out after losing to fellow Americans.
Cressy was beaten 6-3 6-4 by J.J. Wolf and Brooksby lost 6-4 4-6 6-1 to Mackenzie McDonald in the only remaining first round match.
Wolf will face seventh-seeded Alexander Bublik in the quarters after the Kazakh beat Frenchman Corentin Moutet 7-5 6-4.
Florence is hosting a tour-level event for the first time since 1994.
At the Gijon Open, second seed Pablo Carreno Busta of Spain sealed a spot in the quarter-finals with a 6-4 7-6 (7-3) victory over Brazilian Thiago Monteiro.
American fifth seed Tommy Paul secured safe passage to the last eight, beating local Nicolas Alvarez Varona 6-3 7-6 (7-3) with Dominic Thiem, Pedro Cachin and Sebastian Korda among the day’s other winners.
― With AAP.
