Goran Pandev's smart 24th-minute opener and a stunning Lasse Schone free-kick eight minutes after the break gave Genoa their first win since the league restart last month and moves them up to 17th.
Davide Nicola's side are a point ahead of 18th-placed Lecce, who could only manage a goalless draw at Cagliari, and four behind Torino in 16th ahead of their trip to Inter Milan on Monday.
Not even Iago Falque's first-half penalty miss at a boiling Luigi Ferraris Stadium could spoil a simple home win over SPAL, who are staring at relegation after their fifth defeat in six since top flight football returned in Italy.
SPAL took their place in Serie A in 2017 for the first time in nearly half a century but have mostly battled the drop since.
Coached since February by former Italy international Luigi Di Biagio, they are rooted to the bottom of the league on 19 points, 11 behind Genoa with six matches remaining.
Sampdoria meanwhile moved up to 14th, six points ahead of Lecce, after coming from behind to secure a win at Udinese that improves the chances of Claudio Ranieri's side staying in the top division.
Ranieri, Samp jubilant
Kevin Lasagna gave the hosts the lead in the 37th minute with his sixth goal in five games, a fine finish after outmuscling Maya Yoshida.
However Fabio Quagliarella volleyed home the leveller in first half stoppage time of his first appearance since the league restart and Federico Bonazzoli put the away side in the lead with a spectacular bicycle kick six minutes from the end after Udinese twice went close.
Manolo Gabbiadini then made absolutely sure in the final seconds with a beautifully judged curling finish to spark jubilation in the Dacia Arena stands between Ranieri and club owner Massimo Ferrero.
Elsewhere Parma came back from two goals down to draw 2-2 at home with Bologna thanks to two stoppage time goals after announcing their entire matchday squad had tested negative for coronavirus a day after a positive result for a staff member.
Danilo's glancing header and a curling effort from Roberto Soriano had Bologna two ahead within 16 minutes at the Ennio Tardini stadium and as the match crept into added time the three points looked secured.
However Jasmin Kurtic pulled one back for the hosts in the 93rd minute and 10th-placed Bologna were left stunned two minutes later when Roberto Inglese prodded home from a few yards out to salvage the unlikeliest of points for Parma, who stay 12th.
Their match wasn't the only one to feature a last gasp equaliser, as Patrick Cutrone scored even later to give Fiorentina a 1-1 draw at home to Hellas Verona.
Davide Faraoni put Verona in the lead in the 18th minute when he connected perfectly with Sofyan Amrabat's lofted pass to crash home a spinning volley.
The away side squandered chances to put themsleves further ahead and were punished in the 96th minute when Cutrone slid home Federico Chiesa's pinpoint through-ball.
Sunday's late game matches two of Italy's form teams, as Napoli host AC Milan with a spot in next season's Europa league at stake.