Immobile, who was surprisingly left out of the team which lost to Napoli a week previously, earned the home side all three points to revive their fading hopes of playing in Europe next season.
Luca Siligardi scored a late consolation for Livorno, who failed to build on their 2-1 win over Bologna last week and faced the possibility of slipping back into the bottom three on Sunday.
Torino were straight onto the attack in the early stages, with Alessio Cerci denied by Francesco Bardi at his near post.
Their pressure was unrelenting and led to a deserved opener in the 25th minute when Cesare Bovo's free-kick was headed inside the near post from eight yards by Immobile.
Bovo went close with a powerful shot from outside the penalty area which Bardi pushed away before Cerci was also denied by an increasingly busy Bardi.
From the resulting corner, Jasmin Kurtic saw his shot blocked with Kamil Glik sending the rebound wide.
There followed a good spell for Livorno as Torino seemed to relax a little, but they woke up again and wasted a chance to double their lead when Cerci failed to place his shot wide enough of Bardi.
It was only a matter of time before Torino grabbed a second goal, and it was Immobile who struck again on the hour mark.
Glik's cross was lifted into Immobile's path by Omar El Kaddouri and, although the German seemed to mishit his shot, the ball looped over Bardi from six yards.
Immobile completed his hat-trick seven minutes later, sealing victory with his best goal of the night, a 25-yard effort beyond Bardi's reach.
Livorno found a consolation in the last minute, as Siligardi volleyed in after Daniele Padelli flapped at a corner.