Looking to bounce back from their 2-0 defeat at Udinese last Sunday, the hosts struck all three goals in the second half.
Parma, who went into the game inspired by their 2-1 win over Chievo in the last round, never threatened Fiorentina goalkeeper Artur Boruc.
Jovetic gave Fiorentina a deserved lead in the 46th minute before Alessio Cerci doubled his team's advantage on the hour mark.
Jovetic added his second with nine minutes remaining.
Fiorentina could have taken an early lead but Cerci's 10-yard effort was kept out by Parma goalkeeper Antonio Mirante.
Mirante was called again to make a save on the half-hour mark to keep out Riccardo Montolivo's bullet strike from outside the area.
Fiorentina were finally rewarded one minute after the restart.
Valon Behrami's cross found Jovetic inside the area and his right-footed effort beat Mirante.
Parma had the first chance in the 56th minute when Ze Eduardo tried his luck from distance only for his effort to go wide.
Parma should have equalised on the hour mark.
Jonathan Biabiany got his head on Abderazak Jadid's cross and his effort went inches wide of the near post.
Fiorentina doubled their lead soon after when Cerci's powerful header from Juan Vargas' cross beat Mirante.
The Viola put the result beyond doubt in the 81st minute.
Houssine Kharja found Jovetic in the area and the Montenegrin struck the ball towards the left corner of goal and out of Mirante's reach.