Vincenzo Montella's Fiorentina had failed to win their past three matches in all competitions and were looking to keep their slim hopes of a top-three finish alive at Stadio Artemio Franchi.
Diamanti had the perfect chance to put them ahead in the second half, but he fluffed his lines from 12 yards.
And Verona made them pay in the 90th minute when Neto made a hash of a routine effort from Lazaros Christodoulopoulos allowing substitute Mounir Obbadi to pounce.
Fiorentina enjoyed the better of the first-half openings and Rafael kept the scores level just before the half-hour mark with a superb save from Alberto Gilardino's near-post flick after the striker got in front of his man to meet Andrea Lazzari's cross from the left.
But while one goalkeeper was hero, the other proved a zero as Neto spilled Christodoulopoulos' effort from the edge of the box and Obaddi was on hand to tap home the winner to move Verona 13 points clear of the drop zone.
