Reported FC Barcelona and Manchester City target Lautaro Martinez resumed duty up front for Inter, as did Milan Skriniar, Victor Moses, Andrea Ranocchia and Cristiano Biraghi in defence.
Christian Eriksen went close to giving Inter the lead after 12 minutes following a loose ball near the area, but Genoa shot-stopper Mattia Perin got down to collect.
Great hold-up play from Romelu Lukaku inside the area towards the half-hour mark resulted with a layoff to an on-rushing Eriksen, who scooped over from close-range.
However, with the half-hour gone Inter took the lead when Lukaku arrived at the back-post to head in off the near post in the 34th minute.
Filip Jagiello nearly levelled four minutes to halftime after seeing his curling free-kick from outside the area flying narrowly past the bottom corner of Samir Handanovic's goal.
No changes from each side following the start of the second half materialised as the visiting side looked to kill off the contest in earnest.
Genoa purposefully kept the Nerazzurri pinned in their own half and on occasion found a few openings which Andrea Pinamonti, playing against his parent club, couldn't profit from.
Alexis Sanchez, Borja Valero and Danilo D'ambrosio entered for the visiting side after 64 minutes, as Antonio Conte looked to see out the contest in grand style.
Sanchez put his side in complete ascendancy in the last seven minutes after meeting Moses' inch-perfect cross from the right to side-foot in off the underside of the bar.
Inter made the points safe after Lukaku showed quick feet to curl into the bottom corner deep in time added on, leading his side back to second spot, four points off Juventus who host Sampdoria on Sunday.