The team are currently at the bottom of Serie A, eight points adrift of safety after failing to win a single game in the top flight, but they were favourites for today's fourth-round tie.
Pavia, who reside in the third tier of Italian football, are four points behind their league leaders Cittadella following a recent slump, but they have suffered defeat in just one of their last eight domestic fixtures.
In today's Coppa Italia meeting, it was a slow start from both sides as the best opportunity of the game fell to Pavia's Tommaso Bellazzini in the 30th minute, but his attempt at goal was saved.
Personnel changes were made to both sides after the break, but neither team were able to break through the deadlock with 70 minutes on the clock.
The game looked to be destined for extra time until Winck found the back of the net one minute into added time.