Italy striker Immobile helped Lazio strengthen their hold on second spot with a fourth straight win by scoring from the spot in the 36th minute at the Stadio Picco to take his league tally in an injury-hit season to 10.
Felipe Anderson won the spot-kick when he went down under Ethan Ampadu's challenge which was harshly judged to be a foul and a bookable offence, the Welshman was sent off late on following his second yellow card.
Anderson doubled the away side's lead six minutes after the break when he finished off a swift-passing move also involving Luis Alberto and Immobile
Anderson's Brazilian compatriot Marcos Antonio ensured Lazio would move 13 points behind runaway league leaders Napoli when he skipped around Spezia goalkeeper Bartlomiej Dragowski and rolled in the third.
The win boosts Lazio's bid for next season's Champions League. They are eight points in front of third-placed local rivals Roma, who host Udinese on Sunday night.
AC Milan are a further point back in fourth and a point behind them, and just outside the top four, are Inter Milan ahead of their Lombardy derby with Monza on Saturday evening.
Spezia sit one place and four points above the relegation zone and will be hoping Napoli continue their march towards first league title since 1990 on Saturday.
Champions-elect Napoli host Verona, who are just inside the drop zone. Napoli coach Luciano Spalletti said that he will have Victor Osimhen available.
Nigeria forward Osimhen has been out injured since the international break but should play a part in Naples in the hope he will be able to start Tuesday's Champions League quarter-final showdown with AC Milan.
Defeat for Spezia also allowed Cremonese to keep dreaming of a great escape after Cyriel Dessers gave the promoted outfit just their third win of the season, 1-0 over Empoli.
Cremonese are 19th, seven points behind Spezia who travel to rock-bottom Sampdoria next weekend.