Luca Toni's first-half goal was the only difference between the two sides but it was enough to seal Palermo's fate while providing a boost in Fiorentina's hopes of reaching Europe's premier club competition next season.
The defeat leaves Palermo five points adrift of Genoa in 17th place with only one game remaining, meaning they are unable to save themselves from dropping to the second tier.
In contrast, the win for Fiorentina sees them close the gap on third-placed AC Milan to a single point, although the Rossoneri can increase that again when they play Roma on Sunday.
Both sides had several chances in the first half before Toni opened the scoring four minutes before the break.
Palermo goalkeeper Stefano Sorrentino denied both Juan Cuadrado and Stefan Jovetic in the opening exchanges before his opposite number blocked Jasmin Kurtic's 30-yard effort seconds later.
Toni almost broke the deadlock in the 38th minute when he headed Manuel Pasqual's cross just over the bar.
However, he did not have to wait long to give Fiorentina their second consecutive win over Serie B-bound opposition, following the midweek triumph over Siena, when he slid in Cuadrado's low cross.
Borja Valero fired in a testing ball from the right flank which was picked up by Cuadrado who fed Toni at the far post.
Fiorentina were unlucky not to double their advantage after the interval when Stefan Jovetic's shot just missed the near post and Valero fired wide from the resulting corner.
Palermo went agonisingly close to pulling back a goal in the last 10 minutes when Ezequiel Munoz's header went inches wide.
That was the nearest they came on a day which ended in disappointment as their relegation was confirmed.