The Argentine's low drive from the edge of the area was fumbled by goalkeeper Alban Lafont in the 69th minute as Atalanta completed a 5-4 aggregate win to continue their remarkable season.
Luis Muriel put Fiorentina ahead after three minutes, slipping the ball past Pierluigi Gollini after being sent clear by Federico Chiesa's incisive pass.
Atalanta levelled 11 minutes later, Josip Ilicic converting a penalty after Gomez went down under a challenge from Federico Ceccherini.
Atalanta, who will meet Lazio in the final on May 15 in Rome, have won the competition once, in 1963 -- the Bergamo club's only major trophy. Fifth in Serie A, they are also challenging for a place in next season's Champions League.
The defeat effectively ended Fiorentina's season as they are 11th in Serie A with no realistic chance of qualifying for Europe and are under no threat of relegation.