Jonathan Biabiany's first-half goal set them on their way and after keeping Verona at bay in the second half, they added a second in stoppage time through Ezequiel Schelotto.
The win left Parma three points ahead of their opponents in sixth place in Serie A, the final Europa League berth.
Parma dominated the opening exchanges, with Marco Marchionni and Antonio Cassano both forcing decent saves from Rafael Andrade inside the first 10 minutes.
Cassano then set up Raffaele Palladino, who shot over, before Verona threatened for the first time when Juan Iturbe shot just wide.
But Parma took the lead moments later when a corner was only half-cleared. Massimo Gobbi mishit his shot but it turned into an effective pass for Biabiany, who flicked it home via the inside of the post.
Andrade attempted to claw the ball out but it had crossed the line and the goal was given.
Iturbe's free-kick was straight at keeper Antonio Mirante, who also saved from Luca Toni before half-time.
Biabiany was off target at the other end and Marchionni was unable to steer Cassano's cross on target as the interval arrived with no further score.
Marchionni missed again early in the second period, Cassano once more the provider, and the latter then shot well over the bar.
Verona then threatened an equaliser in a 15-minute spell of pressure, starting when Vangelis Moras headed Romulo's free-kick wide.
Romulo picked out Toni with another cross but the former Italy striker headed straight at Mirante.
Domenici Mayetti headed over and Romulo sent an effort high and wide as the visitors' challenge petered out and it was Parma who instead went in search of further goals.
Another instinctive effort from Biabiani skimmed the outside of a post and he then headed over from a cross by the impressive Cassano.
In stoppage time, they were gifted the second goal when Andrade was caught in possession by Cassano. The forward was denied a deserved goal by the post but the ball rebounded for Schelotto to head home.