The match got off to a quick start with Lorenzo Colombo smashing a shot over the crossbar and Nicolo Barella seeing an attempt blocked during the opening exchanges.
Inter then asked questions through Federico Dimarco corners, although Justin Bijlow saved Stefan de Vrij’s header, and Manuel Akanji was unable to hit the target with his attempt.
Bijlow was then called into action again and made a brilliant save to deny Ange-Yoan Bonny after Ruslan Malinovskyi had cheaply conceded possession.
The Nerazzurri were very patient in their play, but Henrikh Mkhitaryan looked to take matters into his own hands and hit an ambitious strike that took a deflection off Johan Vasquez on its way to hitting the crossbar.
Bonny’s header then brought another superb save out of Bijlow, but there was nothing the Dutchman could do on the half-hour when Dimarco emphatically volleyed Mkhitaryan’s looping pass into the far corner from an outrageously tight angle.
Barella then headed over before Mikael Egill Ellertsson’s volley was denied at the other end as the hosts maintained their lead going into the break.
Both teams had promising moves without initially working the opposition goalkeeper after the restart, although Vitinha’s shot from range just before the hour mark required an Akanji deflection to ensure it didn’t hit the target.
Ellertsson then ballooned a header over with Il Grifone looking increasingly encouraged. That didn’t last too much longer, though, as Bijlow made yet another impressive save after Luis Henrique’s shot took a deflection off Aaron Martin.
However, Alex Amorim handled to concede a penalty moments later, and Hakan Calhanoglu sent the Genoa goalkeeper the wrong way from the spot.
Ellertsson sent his latest header wide before Yann Sommer was able to prevent Akanji from scoring an own goal, as Inter avoided any late nerves on their way to recording their eighth consecutive win in Serie A to go 13 points ahead of second-placed AC Milan ahead of their match against Cremonese on Sunday.
In doing so, the Nerazzurri inflicted the first defeat from Genoa’s last three games and left Il Grifone three points above the relegation zone.
Flashscore Man of the Match: Federico Dimarco (Inter Milan)