Gomez opened the scoring as early as the eighth minute to set Rolando Maran's men on their way before Francesco Lodi netted from the spot midway through the first-half.
Catania were out of sight after 28 minutes when Gomez netted from close range and the Argentinian teed up Pablo Barrientos to seal the rout after the interval.
The victory was Catania's fourth victory from six matches at the Stadio Angelo Massimino while Lazio's wretched run continues.
Having been among the early leaders, Lazio's Serie A title challenge had been undermined by three games without a win before Sunday but the result in Sicily must heavily damage morale within the camp.
They fell behind in the eighth minute when Gomez dribbled into the box before drilling past compatriot Albano Bizzarri.
The Lazio keeper kept the deficit to just one goal by saving from Barrientos' low effort but the visitors then did themselves no favours when Andre Dias was adjudged to have handled inside the area in the 25th minute.
Lodi made no mistake with his spot-kick, slotting in the bottom right and Lazio's afternoon went from bad to worse when Gomez converted from Giovanni Marchese's left-wing cross three minutes later.
To their credit, the Biancocelesti refused to let their heads drop and midfielder Antonio Candreva was denied by Catania keeper Mariano Andujar.
They continued to attack after the interval and although Sergio Floccari went past defender Nicola Legrottaglie, Andujar collected the ball from the striker's feet.
Gomez was continuing to cause all sorts of problems and he picked out Souleymane Doukara, whose flick-on produced a fine save from Bizzarri.
There was nothing the Lazio keeper could do, however, when Gomez found Barrientos, who fired low into the net in the 69th minute.
Andujar produced a marvellous save from Candreva's effort outside the area to deny Vladimir Petkovic's men a consolation while their misery was nearly compounded in the final minute but Legrottaglie's header skimmed the bar.