Yuto Nagatomo and Rodrigo Palacio scored second-half goals to hand Inter all three points in a low-key encounter.
Substitute Mauro Icardi also hit the bar in the final stages as Inter's dominance began to tell.
Manager Walter Mazzarri made one change from the Inter side that defeated Citadella in last week's Coppa Italia, with Zdravko Kuzmanovic replacing Icardi.
Fabio Liverani named two changes from last week's Coppa Italia exit at the hands of Spezia, with Juraj Kucka and Andrea Bertolacci coming in for Davide Biondini and Moussa Konate.
The hosts had the only half chance of an uneventful opening quarter, Andrea Ranocchia heading wide from a right-wing corner in the 13th minute.
Jonathan went close for Inter midway through the half, turning inside the box before flashing a shot across goal and just wide of the left-hand post.
Five minutes later, Francesco Lodi had Genoa's first strike on goal, but his effort from 30 yards was dragged well wide.
Inter dominated possession for the remainder of the half, but failed to create a goalscoring opportunity of any note.
The hosts picked up where they left off in the second period as Daniele Portanova had to be alert to cut out Fredy Guarin's cross with Ricardo Alvarez poised to tap home.
Seven minutes into the half, Icardi came on in place of Kuzmanovic and was immediately involved, heading a Hugo Campagnaro cross straight at Mattia Perin in the Genoa goal.
Inter continued to press and almost took the lead shortly before the hour mark as Guarin drove forward down the right-hand channel before firing across goal and narrowly wide.
Gaurin threatened again in the 70th minute, this time seeing his shot from distance comfortably collected by Perin.
Inter finally broke the deadlock in the 75th minute, as Jonathan's cross was deflected over everyone to the back post where Nagatomo was on hand to nod home from a matter of inches.
Inter almost doubled their lead twice in as many minutes shortly afterwards.
First, Icardi hit the crossbar with a header before Perin had to scramble to his right to keep out another header, this time from Ranocchia.
Jonathan then saw his effort from the corner of the box deflected wide as Inter looked for a second to kill the game off.
The goal duly arrived in stoppage time, as Palacio ran on to Guarin's through ball before slotting beyond Perin as Inter sealed their victory in style.
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