Samp won 2-1 with both teams converting penalties on the night.
Fabio Depaoli won a penalty for Samp after being fouled by Rolando Mandragora with Fabio Quagliarella scoring from the spot.
Mandragora then converted a penalty for Toro thanks to Julian Chabot tripping Karol Linetty.
But Samp fought back as Valerio Verre hit a superb second goal for the hosts to help secure the win.
Samp will meet Juventus in the round of 16.
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