The 32-year-old got the only goal of the game to help his side to a vital away win in the battle for the European places in Serie A.
Both sides created a number of chances to break the deadlock, yet it took until the 87th minute for Joaquin to find the net with a good header.
Napoli started the match with attacking intentions, and Gonzalo Higuain almost opened the scoring after 10 minutes. The Argentine latched on to a long ball from Pepe Reina, but Neto pulled off a superb save to deny the former Real Madrid striker.
The hosts continued to dominate proceedings and again threatened through Marek Hamsik midway through the first half, yet Neto once more proved to be too much of an obstacle as he kept out the Slovakian midfielder's attempt from close range.
Rafa Benitez's side was then dealt a major blow in the 37th minute when Faouzi Ghoulam received a straight red card for a foul on Marko Bakic, who was clean through on Reina.
Jose Callejon was the next Napoli player to try his luck, with the Spaniard unleashing an ambitious long-range strike from midfield that nearly surprised Neto, but the Fiorentina goalkeeper was back on his line just in time to keep the ball out.
Fiorentina took over the initiative in the second half and Josip Ilicic should have broken the deadlock in the 64th minute. The attacking midfielder surprised the Napoli defense with a smart run, only to see his shot from a narrow angle go inches wide.
The guests got another big chance shortly after when Borja Valero found Alessandro Matri with a fine cross, but the striker's header was too weak to trouble Reina.
Vincenzo Montella's side would go 1-0 up in the closing stages of the game, however. Matri set up Ilicic down the left wing, whose cross found Joaquin inside the area, and the Spanish winger headed home from close range to help the Viola to victory.
Napoli remains third in the Serie A table with 58 points from 29 games, while Fiorentina sit fourth on 51 points.