Domenico Di Carlo's men headed into the encounter at the Stadio Alberto Picco having won none of their previous eight games, but just as they did when they met the Garnets earlier in the campaign, they ran out victors to halt their poor run of form.
It proved to be a mixed outing for Spezia's former Napoli centre-forward Emanuele Calaio, who broke the deadlock in the 13th minute when he back-heeled the ball beyond the reach of visiting goalkeeper Pietro Terracciano following a through pass from Josip Brezovec.
However, within the space of five second-half minutes the 33-year-old former Italy youth international was cautioned twice and subsequently red-carded, leaving his side to see out the remainder of the tie a man light.
By that point the hosts were already two goals in front courtesy of centre-back Sergio Postigo's second goal of the season in the 33rd minute. The visitors failed to fully clear a corner and having wriggled himself free to find enough space inside the area, the Spanish centre-back fired his shot into the roof of Terracciano's net from close range.
To make matters worse for the away side, like Spezia they also ended the contest with 10 men when substitute Umberto Eusepi was handed his marching orders for a foul on Brezovec in the last minute.