Czech defender Zdenek Grygera charged into the box after a lay-off from Alessandro Del Piero and found the far bottom corner from a tight angle to give the hosts the lead in the sixth minute.
Brazilian striker Amauri doubled the advantage 20 minutes later, soaring to head in a Grygera cross from the right with power, before substitute Vincenzo Iaquinta made it 3-0 with a cool finish in the 85th.
Diego Milito pulled one back for Genoa with a penalty only for Sokratis Papastathopoulos to divert a Mauro Camoranesi cross from the right into his own net in stoppage time.
Juventus's seventh consecutive victory in all competitions gives them 24 points from 12 league games, the same tally Inter notched in 11.
Genoa responded positively to the early setback, with defender Matteo Ferrari nodding just over the bar and Milito coming close after sending his markers dizzy with some superb dribbling.
They also kept pressing after Amauri scored against the run of play and Raffaele Palladino spurned a great chance to score four minutes after the break.
But they seemed to lose heart as their efforts went unrewarded and Juventus eventually romped home amid a late goal flurry.
Thursday's game was brought forward from this weekend's Serie A programme because the Italy rugby team are playing Argentina at Turin's Stadio Olimpico on Saturday.
