A dull game was brought to life in the second period when Inter took the lead through a Francesco Vicari own goal, only for Paloschi to deny Inter victory and secure a vital point for his side.
The result leaves Inter without a win in five, having failed to restore the pressure on the top four, while SPAL are now just a point adrift of safety.
Neither side had notable chances to take the lead in the first period, but Antonio Candreva had the game's opening opportunity. The Italian's low shot was parried by SPAL goalkeeper Alex Meret, before the stopper smothered the resultant cross.
Meret, who was debuting after joining on loan from Udinese, continued to impress in the hosts' goal, and took hold of two Candreva crosses that were harmlessly headed back into the box by Ivan Perisic, who had no-one in support on either occasion.
The first half petered out following Candreva's initial effort, however, and the only openings thereafter saw Alberto Grassi head over from Mirco Antenucci's cross, before Samir Handanovic made a simple save down low from Antenucci's shot.
Despite Meret's solid display in the first period, his good work was undone by defender Francesco Vicari, who got a goal-bound touch to a curling cross that left the goalkeeper staring and gave an Inter an unlikely lead.
The opening goal brought the game to life, with both sides producing chances to find the net in the latter stages of the game.
SPAL had their share of opportunities to grab an equaliser, with Jasmin Kurtic wasting good chances to find the net. The Slovenian failed to steer a header goalwards under pressure from Miranda, before he had space from a cross but blasted an effort high and wide.
Mauro Icardi, who has scored 18 league goals this term, could have made it 19 when he failed to make contact with a corner flicked on by the head of Vecino.
SPAL did equalise when Paloschi, who had replaced Pasquale Schiattarella, steered a diving header past a motionless Handanovic.
SPAL (3-5-1-1): Meret; Cionek, Vicari (Bonazzoli, 86), Felipe; Lazzari, Schiattarella (Paloschi, 75), Viviani, Grassi, Mattiello (Costa, 83); Kurtic; Antenucci
INTER MILAN (4-2-3-1): Handanovic; D'Ambrosio, Skriniar, Miranda, Concelo; Vecino, Valero (Rafinha, 90); Candreva (Eder, 45), Brozovic (Gagliardini, 87), Perisic; Icardi