The Argentine had not featured since being stripped of the captaincy on February 13 amid protracted contract renewal talks.
Icardi initially said he could not play because of a knee problem.
But he returned to training last week after negotiations between his lawyer and the club.
Roberto Gagliardini opened the scoring in the first half before Icardi won and converted a penalty after Genoa defender Cristian Romero was sent off.
The former Inter captain then teed up Ivan Perisic for their third in the second half and Gagliardini scored his second of the night to complete the rout.
The result leaves Inter four points clear of fourth-placed rivals AC Milan, while Genoa remain 12th on 33 points.
Prior to the game, Inter boss Luciano Spalletti had said of Icardi: ‘
For us, he’s a player to follow if he is one metre ahead. We’re stronger with him now. Whoever says we’re weaker are against us.
‘The case is closed in all respects. Now he needs to train, sweat, smell the grass and not talk through other people.’