Simone Inzaghi's side bounced back from a home defeat to Inter Milan to move ahead of AC Milan, who play in Udinese later Sunday.
Lazio with 21 points from 11 games are ten points behind leaders Juventus, who continued their unbeaten run with a 3-1 win over Cagliari on Saturday.
Italian international Immobile volleyed in the first after 26 minutes off a Cataldi corner, past SPAL goalkeeper Vanja Milinkovic-Savic, brother of Lazio midfielder Sergej, who was also playing at the Stadio Olimpico.
But the celebrations were short lived with Mirco Antenucci tapping in the equaliser for SPAL two minutes later.
Blunders by SPAL's Brazilian defender Everton Luiz allowed Cataldi and Parolo to break through in the second half, but Immobile was denied a hat-trick by the woodwork.
SPAL, a club from Ferrara in Emilia-Romagna, stay 15th after their seventh defeat of the season.
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