Gasperini lost his first two matches after taking charge a month ago, but today's [Sunday] draw means that since then Palermo have earned five points from three outings.
Palermo started the better at the Stadio Renzo Barbera, but home goalkeeper Samir Ujkani was the busier of the two custodians after the break as Torino pushed for their third win of the season.
Palermo's Slovenia forward Jasmin Kurtic was first to threaten with a 12th-minute effort that was saved by Jean Francois Gillet.
Josip Ilicic and Massimo Donati then fired wide for the home side before Gillet produced a fine save to keep out an Ilicic shot that was heading for the top corner.
Torino finally showed an attacking threat toward the end of the first half, Rolando Bianchi giving Ujkani an easy save in the 42nd minute, and the visitors built on that after the break with Bianchi again testing the Palermo keeper.
Paraguay international Edgar Barreto fired just wide as Palermo countered, but Ujkani was back in action in the 72nd minute with a good save to keep out Meggiorini's close-range attempt.
Torino midfielder Giuseppe Vives then flashed a shot inches wide of the left-hand post before Ujkani was again called upon to keep out Salvatore Masiello's 83rd-minute effort.
The final chance of the match fell to Ilicic, but his shot from the right-hand side of the box flew just wide of the far post as the spoils were shared.