Meanwhile, second-place Roma eased to a 2-0 win at struggling Chievo Verona. Roma was 11 points behind leader Juventus and six ahead of third-place Napoli.
Immobile scored his first in the 25th minute, heading in Cesare Bovo's free kick, and the second on the hour mark after Francesco Bardi proved staunch in the Livorno goal. Immobile mishit Omar El Kaddouri's pass but the ball's bounce deceived Bardi.
The forward, co-owned by Juventus, completed his first Serie A hat trick seven minutes later with a great shot from distance for his 16th goal of the season.
Immobile was given a standing ovation when he was substituted with 13 minutes remaining. He's a contender for Italy coach Cesare Prandelli's World Cup squad.
"I'm proud and happy with this hat trick, I didn't even do it at Pescara and I'm taking the match ball home," Immobile said. "Prandelli knows me, he knows how I work and if he calls me up I'll be ready."
Luca Siligardi volleyed home a consolation for Livorno in the final minute.
Torino reignited its European hopes as it ended a run of four consecutive defeats, although it was provisionally seven points behind sixth spot.
Livorno remained a point above the relegation zone, ahead of the rest of the weekend's matches.
It was equally easy for Roma, which was never troubled by Chievo.
Chievo gifted Roma the lead in the 17th minute when Bostjan Cesar's header back to goalkeeper Michael Agazzi was too weak and was easily intercepted by Gervinho, who slotted calmly home.
Mattia Destro doubled Roma's lead three minutes from halftime, firing Rodrigo Taddei's delightful throughball into the bottom right corner.