The start of the match was delayed due to dense fog at the Alberto Braglia Stadium, but it eventually got underway after the referee deemed that play could go ahead.
Neither side were able to find a breakthrough in the first half as clear-cut opportunities were hard to come by due to a lack of quality in the final third.
Carpi were handed the opportunity to extend their lead when Marco Borriello was brought down in the penalty area, which resulted in a spot kick being awarded and the dismissal of Vicenza defender Mario Sampirisi.
Borriello took the penalty and buried his effort into the net to put his side in control of the match.
Vicenza put the pressure on towards the end of the match, but the home side held out for the victory to advance to the next round of the competition.