The Italy international scored two and created the third against an off-colour Genoa, who slumped to their second straight defeat.
Giovinco scored his first in the 29th minute before adding a second from the penalty spot in the 42nd minute. He then turned provider for the third goal, scored by captain Stefano Morrone in the 50th minute.
Rodrigo Palacio scored a consolation for Genoa with the final kick of the game from the penalty spot.
Giovinco was Parma's hero in their previous win this season with both goals in a 2-1 win over Chievo and he made the difference once again.
His first goal came when he latched onto Sergio Floccari's neat pass and beat Cesare Bovo with a good first touch before shooting past Sebastien Frey into the roof of the net.
Bovo almost made amends for his mistake two minutes later but Antonio Mirante pushed his free-kick against the post and Alessandro Lucarelli cleared the loose ball ahead of Palacio.
Giovinco then earned and converted a penalty to make it 2-0. He stole the ball off Miguel Veloso out wide and then dribbled into the area, where he was fouled by Jurak Kucka.
The diminutive Italian set up the third, his cross headed back into the centre by Jonathan Biabiany to Morrone, whose first header hit the crossbar but returned to him to nod in.
In stoppage time, Gabriel Paletta tugged Palacio's shirt inside the penalty area and the Argentinian converted from the spot to join Giovinco on five goals for the season.