Juan Cuadrado gave the Viola the lead in the 11th minute before Alessandro Matri doubled their advantage before the break.
Alberto Paloschi took his third big chance of the match to reduce the arrears, but it was not enough as, after David Pizarro missed a penalty for the hosts, Gomez notched his first goal on home soil to seal the win for the hosts.
Not only had Fiorentina lost their grasp on fourth on Saturday night when Inter Milan defeated Hellas Verona, but they had dropped to sixth on Sunday afternoon when Parma beat AC Milan.
Only 11 minutes in, they were on their back up to the top four when Cuadrado pulled the ball back to Pizarro before bursting through to latch onto the return pass, taking it first time on the volley to lob Michael Agazzi.
Chievo responded well and Paloschi wasted two excellent chances to bring them level, first flicking Adrian Stoian's cross wide before shooting straight at Neto with only the Fiorentina custodian to beat.
Just before half-time, the hosts created a bit of breathing space for themselves when Anderson threaded a pass through for Cuadrado, whose cross from near the goal line was turned in from close range by Matri.
Chievo did not lose belief, though, and Paloschi finally got his goal on the hour mark, taking the ball past Neto and lifting his shot into the top left-hand corner.
After a brief spell in which Chievo threatened an equaliser, Fiorentina had the chance to wrap up victory when Matteo Rubin handled the ball inside the area and a penalty was awarded.
Agazzi dived to his left and turned Pizarro's spot-kick wide, though, to keep Chievo in the game.
Their lingering hopes were finally dashed in the 89th minute when Gomez was put through by Josip Ilicic and slotted the ball through the legs of Agazzi, although he was fortunate that the offside flag was not raised as the German celebrated in front of the Viola fans for the first time.