Genoa thought they might have done enough to avoid an embarrassing early exit to lowly Spezia when Francesco Lodi forced extra time in Liguria - but it was the Serie B side who triumphed on penalties.
Italy striker Alberto Gilardino opened the scoring on the west coast but Lega Pro Prima Divisione champions Spezia hit back through Marco Sansovini and Osarieman Ebagua to lead 2-1 heading towards full-time.
Lodi converted a spot-kick deep into stoppage time but Genoa could not find a winner in time added on and duly lost the shootout.
Next up for Spezia is a trip to Pescara, who returned from Torino as 2-1 winners.
The top-flight club answered Riccardo Maniero's goal through Ciro Immobile but Antonino Ragusa settled the tie in the Delfini's favour on the hour mark.
Lega Pro side Frosinone produced another shock against Cagliari in their temporary Trieste base.
The Canarini forced extra time at the Stadio Nereo Rocco and Davis Curiale's goal on 120 minutes ensured a 2-1 win over the exiled Sardinians.
Recently-relegated Siena also stunned top-flight opposition as Angelo's first-half goal decided a 1-0 victory over Tuscan rivals Livorno.
The Bianconeri, who narrowly avoided bankruptcy this summer, will next face Bologna, who beat Brescia 1-0 at the Stadio Renato dall'Ara.
Antonio Cassano scored a debut goal for Parma in an easy 4-0 victory over Lega Pro side Lecce. The former AC Milan and Roma striker was joined on the scoresheet by Amauri, Gianni Munari and Raffaele Palladino.
Sampdoria will host Hellas Verona in the fourth round after Manolo Gabbiadini's brace decided a 2-0 win over Benevento at the Marassi while the newly-promoted Gialloblu downed Palermo 1-0 in Sicily.
Chievo beat Empoli 2-0 to earn a home meeting with Reggina, who ousted Crotone 1-0, while Avellino's victory by the same scoreline over Cesena set up their trip to Frosinone.
Games at Novara and Juve Stabia also went to 120 minutes and Sassuolo raised their game to beat the former side 3-1 while Stabia beat Varese on penalties.
Sunday's ties see Inter Milan welcome Cittadella to San Siro - the Nerazzurri find themselves in the unusual position of not being among the top-eight seeds after finishing ninth last season - while Atalanta tackle Bari in Bergamo.
Trapani await the winner of Inter's game after beating Padova 1-0 and Sassuolo will play Atalanta or Bari.