Luciano Spalletti's side notched up their seventh straight Serie A win to move three points behind champions Juventus, who host Cagliari later on Saturday, and equal on points with Napoli who eased past Empoli 5-1 on Friday.
Top scorer Mauro Icardi was rested with an eye towards Tuesday's game in the San Siro after Inter lost 2-0 to Barcelona in the away leg.
But the team shrugged off the absence of their skipper as Gagliardini scored in either half. Portuguese midfielder Joao Mario capped an impressive individual performance by scoring the fourth goals and setting up three others, including for Matteo Politano and fit-again Radja Nianggolan.
"After a difficult start to the season, I needed a boost," said Gagliardini. "I'll try to continue like this. It is tough not playing often, but Inter are doing well and we are all happy about that."
The Italian fired in the first from close range after 14 minutes after a cross from Mario who then found a way through for Politano to sneak in a second two minutes later.
Gagliardini followed his first goal of the season with his first Serie A brace just after the break. The second came from a rebound after Genoa goalkeeper Andrei Radu had cleared an Ivan Perisic effort off the line.
Mario then broke through to score in injury time drilling a low shot into the corner of the net before setting up late substitute Nainggolan, back from an ankle injury, who headed in the final action of the night.
"The most satisfying thing was to see the 70,000 in the stadium today applauding and pleased with our performance," said Spalletti who praised Gagliardini's attitude.
"When I left Gagliardini out against Lazio, he was clearly disappointed. He is off the Champions League squad list too but he showed how much he wants to help the team.
"If Gagliardini had come to training with that disappointment and lowered his head, then he wouldn't have performed like this.
"He was rewarded for his professionalism and we have several players like that, most evidently Joao Mario, but also Dalbert who did well today."
Genoa, meanwhile, have now gone four games without a win as they sit midtable with 14 points from ten games.