A fourth consecutive win saw Maurizio Sarri's men tighten their grip on second spot. They are a provisional 13 points adrift of Napoli and eight points clear of AS Roma in third.
Lazio have now kept a clean sheet in their last five away league games, equalling the club's record set in 1998 under Sven-Goran Eriksson.
Spezia could have shocked the visitors by taking an early lead through midfielder Mehdi Bourabia, whose close-range effort hit the bar inside the opening two minutes.
Ten minutes later Spezia striker M'Bala Nzola had a good chance but his header bounced in front of goal and went wide.
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 by Ethan Ampadu.
Immobile, sidelined during most of March through injury, brought up his 10th league goal of the season and first since his double in the 2-0 win at Salernitana on Feb. 19.
Lazio looked determined to score again before halftime but Immobile and Anderson missed from close range and a shot from the edge of the box by Sergej Milinkovic-Savic was saved by Dragowski.
ANDERSON STRIKES
Sarri's side, however, did double their advantage seven minutes into the second half through a low shot by Anderson.
The Brazilian has made 28 out of 30 starting lineups in Serie A this season but had failed to score for more than two months.
Lazio, on top for most of the game, dominated the hosts in the closing 15 minutes and another goal seemed a matter of time.
Antonio eventually wrapped up a comfortable win in the 89th with his first goal for Lazio less than 10 minutes after coming on.
The 22-year-old showed speed and control as he beat two defenders and the keeper before netting with a low strike.
Spezia finished with 10 men after defender Ampadu got a second yellow for fouling winger Mattia Zaccagni six minutes from time.
They are in 17th place on 26 points and remain four points above the relegation zone.
Second-bottom Cremonese beat visiting Empoli 1-0 earlier on Friday after a fourth-minute goal by forward Cyriel Dessers.
