Dybala stepped into the void left by an injury to Fabrizio Miccoli and scored twice in the second half, going close to completing his hat-trick too as he earned the Sicilians all three points.
Sampdoria's seventh defeat in a row now leaves the future of their coach Ciro Ferrara unclear as the Blucerchiati go into next weekend's city derby with Genoa knowing it is a battle against relegation, as well as pride.
Without Miccoli, Palermo lacked their most identifying figure, but a teenager stepped forward to fill that void.
Dybala, who turns 19 on Thursday, had appeared five times for the Rosaneri already this season without finding the back of the net, but he made up for that to become the new darling of the Sicilian side's faithful.
He missed a first chance after half an hour before showing the battling characteristics to endear him to the home fans 10 minutes later when Edgar Barreto went close to breaking the deadlock.
Just a minute later, Dybala was denied his first goal in Serie A only by Sergio Romero's left leg, which did enough to send the young Argentinian's shot looping over the crossbar.
He needed just seven minutes of the second half to finally break his own duck and put Palermo in front.
Half-time substitute Mauricio Pinilla pulled the ball back from the goal line for him and he showed a confidence which defies his age with a well-placed shot inside the near post and into the top corner.
In the 71st minute, he again demonstrated a high level of confidence with the ball as he turned and picked his spot in the far corner rather than returning the ball to Pinilla, who had moved into a dangerous position alongside him.
In the last minute, he showed another aspect of his game - his electrifying pace - as he surged clear of the Samp defence only to see his goalbound shot pushed wide by his compatriot.
A standing ovation was reserved for him in stoppage time with Miccoli leading the applause as he was substituted by Gian Piero Gasperini at the end of a game in which he had single-handedly earned Palermo all three points.