Romelu Lukaku scored after just 32 seconds and was then involved as Matteo Darmian and Alexis Sanchez added second-half strikes.
The result sees Inter move seven points above Milan - who play Roma on Sunday evening - and 10 points above Juventus.
So which players stood out at San Siro?
✔️ LAUTARO MARTINEZ: 7.1
Lautaro didn't manage to score this time around but he once again showed why his forward partnership with Lukaku is perhaps the most feared in Europe.
He assisted Lukaku's goal, while he was denied twice himself by Perin.
The Argentine had a game-high 14 touches in the box as he was involved in many of Inter's best moments.
✔️ MATTEO DARMIAN: 8.1
Darmian has been a surprise success story at Inter this season since his move from Parma last summer.
And he was relentless in this win against Genoa as he never stopped bombing up and down the right-side all match long.
He doubled Inter's lead in the 70th minute with a clinical finish and had an impressive three shots in total during the game. He also had fine defensive stats, winning three of his four tackles and eight of his 10 duels.
⭐ Romelu Lukaku: 8.6
The Belgian striker is simply unstoppable right now - and it took him just 32 seconds to break the deadlock on Sunday. He burst through the middle and blasted a low drive into the bottom corner with his weaker right-foot.
Lukaku had an incredible five shots in the first half alone - and seven in total - as he continually caused problems to the Genoa backline with his strength and speed. He now has 18 Serie A goals this season - and 24 in just 31 appearances in all competitions.
Lukaku also provided the assist for Darmian with 20 minutes remaining, while his shot that was saved by Perin resulted in Alexis heading home a third.