The 33-year-old former Arsenal and AS Roma player put the Crusaders ahead after 10 minutes, collecting a through ball from Juraj Kucka and comfortably beating Genoa goalkeeper Alberto Paleari who was making his Serie A debut.
Having fired wide from close range and then struck the crossbar before halftime, Gervinho pounced on a mistake in the in the Genoa defence to add the second two minutes after the break.
Eldor Shomurodov pulled one back in the 50th minute amid protests from Parma coach Fabio Liverani who claimed there was a foul in the build up.
Parma's second win of the season left them 16th with nine points while Genoa are one off the bottom with five.
After having an early goal disallowed for offside, Andrea Belotti gave Torino the lead in the 25th minute with his seventh league goal of the season and his 99th for the club.
Sampdoria are eleventh with 11 points and Torino 18th with six.
"It's very disappointing, I see this team improving every day but we need to take the extra step," said Belotti.
"We create chances but we can't bring home the three points -- maybe there will come a moment when the games will turn in our favour."