The home side took the lead in the 25th minute when Cesar Bovo found Immobile in the box, and he slotted the ball past Francesco Bardi.
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Immobile got his second of the game in the 60th minute when he found the net after being teed up by Omar El Kaddouri.
The 24-year-old completed his hat-trick seven minutes later when he converted from close range after latching onto a pass from Jasmin Kurtic.
Livorno got a late consolation through Luca Siligardi, but the hosts held out for the comfortable victory to move up to 10th in the table.