Venezia needed to fight back against Frosinone in the First Round of the Coppa Italia and squeezed through on penalties to set up a meeting with Bologna or Ternana.
The Lagunari gave Mattia Caldara his debut in defence and lost Domen Crnigoj to a hand injury just five minutes in.
Frosinone rattled the woodwork through Camillo Ciano and Marcus Rohden missed a sitter, not to mention a chaotic move that saw Caldara practically clear off the line.
The Canarini did eventually take a deserved lead in extra time, Ciano nodding on a corner for Mirko Gori to tap in at the back post.
However, Pezemyslaw Szyminsky brought down Johnson for a penalty, converted by Francesco Di Mariano.
It went to penalties, with Raffaele Maiello, Tanner Tessman and Federico Gatti spot-kicks saved, Tyronne Ebuehi converting the decisive effort in sudden death.
Venezia 1-1 Frosinone (9-8 on pens)
Gori 93 (F), Di Mariano pen 101 (V)