Luca Antonelli gave the Genovese side the lead in the 14th minute, and after Giuseppe Bellusci was sent off shortly before the break, there was only going to be one winner.
Genoa had to wait until five minutes from time before sealing victory, though, with 20-year-old Stefano Sturaro's first strike in Serie A settling their nerves and ending Catania's hopes.
Genoa pressed straight away in search of a win which should put any lingering relegation hopes to bed.
It took them 14 minutes to open the scoring, with Antonelli getting a lucky break off a Catania defender to shoot against Mariano Andujar before a second stroke of fortune came from his own team-mate Alberto Gilardino with the rebound falling kindly for him to sweep in at the far post.
The hosts warranted their lead and went close to increasing it with Pape Konate's piledriver which just missed the target, much to Andujar's relief.
Bellusci picked up a yellow card and almost talked himself into a second as he refused to watch as the referee extracted the card.
It was not long before he got to see both colours of card in the referee's top pocket as a foul on Marco Motta earned him an early bath in the 39th minute, reducing Catania to 10 men and further reducing their hopes of recovering.
They could count themselves lucky not to be further behind at the break too when Gilardino slid in to meet Motta's cross two minutes before half-time, but he was unable to increase Genoa's advantage going into the break.
A free-kick from Ioannis Fetfatzidis was pushed away by Andujar as Genoa continued to look for the comfort of a second goal, not relying on their one-goal lead, even against 10 men.
They almost got it in the 80th minute when Gilardino failed in a one-on-one with Andujar, but it finally arrived five minutes later when Sturaro beat Andujar with a shot from just outside the area - his first goal in Serie A.
It settled Genoa's nerves and was enough to seal all three points for Gian Piero Gasperini's men.