It was only Pescara's second victory in front of their own fans this season, coming much to the relief of their under-fire coach Giovanni Stroppa, with both goals arriving in the second half.
Parma missed the chance to join Fiorentina in fifth place as their three-game winning streak came to an end in Abruzzo.
Marco Capuano missed the first chance for a sprightly home team when he turned and shot over the bar in the 25th minute.
Parma showed the confidence accrued from three straight wins with Jonathan Biabiany shooting over the bar and then beating Pescara goalkeeper Mattia Perin, whose blushes were saved by a covering defender.
Abbruscato created another good opening just before half time when he put Alessandro Lucarelli under pressure and took the ball to the goal-line, but his cut-back was cleared behind for a corner.
Abbruscato then scored his first goal of the season four minutes into the second half when he held off the challenge of Gabriele Paletta before picking his spot in the far corner.
The last time the much-travelled striker scored was in Serie B for Vicenza in January.
Lucarelli responded for Parma, but Perin pushed the Parma defender's header away at full stretch in the 51st minute.
Parma improved, but found Perin in fine form to keep them out while Pescara waited for chances to arrive on the counter attack.
Weiss was inches away from scoring from one of these before sealing the victory deep into stoppage time with a fine individual effort, using pace and strength to carry the ball 30 yards before dispatching it in off the inside of the right-hand post.