The smattering of fans at the Stadio Luigi Ferraris had to wait until midway through the second half for Lukaku to open the scoring, then late in the game D’Ambrosio was in the right place, at the right time to double Inter’s lead.
Inter made it five consecutive clean sheets against Genoa, thus equalling a record against a single opponent with Atalanta being the other team when the managed the same feat between 1951 and 1953.
As a result, Inter move provisionally third in the Serie A table, with Genoa in 11th position on four points.
It was all Inter from the off, as the Nerazzurri had Genoa pinned in their own half, but they were unable to create anything clear cut.
In fact, it was Genoa who had the best chance initially when Goran Pandev found himself in on goal, doing well to stay onside, but a poor touch as he drove towards goal saw the ball roll harmlessly out of play.
There was plenty of pressure from Inter, but Genoa remained resolute. Arturo Vidal went close after Lautaro Martinez blazed just over the bar from 18 yards.
Incidentally it was the first time that Inter have failed to have a shot on target in the first half in Antonio Conte’s reign as coach.
After the break it was more of the same from Inter as they kept knocking on the Genoa door, and it took until just after the hour mark for Lukaku to break the deadlock.
Some nice combination play between the Belgian and substitute Nicolo Barella allowed Lukaku into the box, before he cut onto his left foot and rifled into the top corner.
Lukaku had a second goal ruled out for offside, just before Lautaro was substituted. The Argentine was visibly angry when taken off and punched his seat a couple of times.
The second goal did come 11 minutes from time as Marcelo Brozovic swung in a corner towards Ranocchia, who has his header poked home by D’Ambrosio.