Second-placed Lazio are 13 points adrift of runaway leaders Napoli and increased their lead over AS Roma in third to eight points.
Lazio opened the scoring in the 36th minute with a coolly taken spot-kick by Immobile, who sent Bartlomiej Dragowski the wrong way after a foul on Anderson in the box by Ethan Ampadu.
Maurizio Sarri's men doubled their advantage seven minutes into the second half through a low shot by Anderson.
Antonio wrapped up a comfortable win in the 89th with his first goal for Lazio less than 10 minutes after coming on.
Spezia finished with 10 men after defender Ampadu got a second yellow for fouling winger Mattia Zaccagni six minutes from time.
Spezia, who are in 17th place on 26 points remain four points above the relegation zone.
AAP
