Vincenzo Montella's men blew away the relegated hosts with a spectacular showing but Milan's late victory over Siena means that they must settle for a place in the Europa League
An Adem Ljajic hat-trick, along with strikes from Matias Fernandez and Stevan Jovetic easily saw off Marco Vittiglio's late consolation effort, and it appeared that they would end their three-year European hiatus at the Rossoneri's expense.
However, it was to be in vain as Massimiliano Allegri's side turned around their match against Siena in the dying embers to disappointingly consign Fiorentina to the group stages of next season's Europa League.
The Tuscans knew that a victory over the basement boys the coupled with AC Milan's inability to beat Siena would result in them securing Italy's last remaining ticket to Europe's elite club competition - ahead of Milan.
And they promptly took the lead after 16 minutes when Ljajic tucked away Juan Cuadrado's cross with a delightful touch.
Not long later, Ljajic doubled his tally in unorthodox fashion as his cross deceived Mattia Perin and crept under the crossbar.
Four minutes later, the goal rush kept coming as Fernandez cut in from the right-hand side and fired home from outside the area.
The half-time break offered welcome respite to the hosts, but under 10 minutes after the restart, Jovetic was on hand to net from a rebound.
The match may have been out of Pescara's reach from the word 'go', but Fiorentina still showed no signs of letting up as Ljajic sealed his hat-trick with another fine strike.
Nevertheless, Pescara did grab a consolation prize via youngster Vittiglio who mopped up Cristiano Lupatelli's parry from Eugenio Togni.