There were slender Coppa Italia victories for Fiorentina, Genoa, Parma and Udinese, but Verona needed penalties to beat Venezia after a 3-3 thriller.
Fiorentina welcomed the first goals for Lorenzo Venuti and Jose Callejon, but Santini performed a stunning overhead kick to get Serie C side Padova back into it at 2-1.
Goalkeeper Emanuele Terracciano had to make a last-gasp save on Nicastro’s header to prevent it going to extra time.
There were slender Coppa Italia victories for Fiorentina, Genoa, Parma and Udinese, but Verona needed penalties to beat Venezia after a 3-3 thriller.
Fiorentina welcomed the first goals for Lorenzo Venuti and Jose Callejon, but Santini performed a stunning overhead kick to get Serie C side Padova back into it at 2-1.
Goalkeeper Emanuele Terracciano had to make a last-gasp save on Nicastro’s header to prevent it going to extra time.
Fiorentina will face Udinese in the Fourth Round, as the Friulani beat Vicenza 3-1 with goals from Fernando Forestieri, Gerard Deulofeu and Ignacio Pussetto.
Genoa set up a fascinating Derby della Lanterna with Sampdoria in the next round, but needed a Gianluca Scamacca brace to get the better of Serie C side Catanzaro.
Parma thanked a Yann Karamoh brace and Andrea Adorante’s late finish to beat Pescara 3-1.
They will face Cosenza in the Fourth Round next month.
Verona were pushed all the way, as they were held 2-2 by Venezia, then it ended 3-3 in extra time, until goalkeeper Pandur took centre stage with two saves in the shoot-out.
SPAL also required penalties to get the better of Serie A outfit Crotone, as it was 0-0 after 90 minutes and 1-1 after 120, so they will face Monza in the next stage.
Crotone 1-1 SPAL (4-5 on pens)
Cigarini pen 107 (C), Seck 113 (S)
Genoa 2-1 Catanzaro
Scamacca 7, 65 (G), Fazio 83 (C)
Hellas Verona 3-3 Venezia (6-4 on pens)
Ilic 41 (HV), Salcedo 59 (HV), Johnsen 84 (V), Capello 87 (V), Modolo 98 (V), Vieira 110 (HV)
Fiorentina 2-1 Padova
Venuti 10 (F), Callejon 32 (F), Santini 55 (P)
Parma 3-1 Pescara
Karamoh 26, 43 (Pa), Adorante 70 (Pa), Nzita 91 (Pe)
Udinese 3-1 Vicenza
Forestieri 21 (U), Deulofeu 60 (U), Pussetto 64 (U), Gori 88 (V)