Both players added to Alberto Aquilani's opener to give the Viola a 3-0 half-time lead at the Stadio Luigi Ferraris.
The second half was more evenly matched, with Alberto Gilardino pulling a goal back and winning the penalty from which Francesco Lodi scored Genoa's second.
But Fiorentina restored their three-goal cushion on each occasion, first through Rossi and then through Gomez - also from the spot - after a frantic finale which saw red cards shown to Genoa's Mario Sampirisi and Viola coach Vincenzo Montella.
Either of the pair could have had a hat-trick, too, and they will both look back with regret on a third-minute opportunity.
Gomez rifled Borja Valero's cross against the post from close range and Rossi extraordinarily ballooned the rebound over the bar.
Aquilani showed them the way in the 10th minute, stooping to head in Valero's corner, and four minutes later Rossi atoned for his earlier howler with a superb long-range volley which found the net despite a touch from keeper Mattia Perin.
Genoa had chances to respond, but Neto twice saved from Gilardino headers.
And the visitors stretched their lead five minutes before the interval when Manuel Pasqual took a pass from the influential Valero and crossed for Gomez to finish at the near post.
Rossi failed to beat Perin on the stroke of half-time and Neto saved from Luca Antonelli early in the second period.
Genoa cut the deficit in the 54th minute when Matuzalem's deft through-ball was brilliantly flicked home on the volley by Gilardino, but a superb long pass by Valero allowed Aquilani to tee up Rossi for an instant reply.
It was 4-2 on the hour when Marvin Compper pulled down Gilardino and Lodi sent Neto the wrong way.
Neto continued to hold the upper hand in his personal battle with the industrious Gilardino and from his latest save, Fiorentina swept straight upfield but Aquilani's shot flashed just wide.
There were chances for either team in the last five minutes, Genoa's Davide Biondini shooting just over before Gomez drilled an effort wide.
Montella was sent to the stands with a minute remaining, and bizarrely responded by walking straight across the pitch.
There was still time for another goal - and another dismissal - as Sampirisi dragged down Matias Fernandez and was shown a second yellow card, Gomez converting the spot-kick.