The men from Turin fell behind to Mauricio Pinilla's strike after 21 minutes - only the second goal Antonio Conte's men have conceded in 11 league games - but a Fernando Llorente brace turned the game on its head before Claudio Marchisio's long-range effort and a tap-in from the impressive Stephan Lichtsteiner.
Cagliari goalscorer Pinilla was then dismissed for dissent late on.
"It's an extraordinary achievement, the fact in the history of Juventus - knowing the teams they had - never managed this before is amazing," coach Conte told Sky Sport Italia.
Genoa's misery was compounded five minutes later when Matuzalem was dismissed for a second bookable offence.
The convincing nature of the win will have been welcomed by coach Rudi Garcia, who saw his side's unbeaten run in the league this season come to an end with a 3-0 defeat to Juve last weekend.
In Sunday's late kick-off, Milan saw a two-goal lead slip through their fingers as they fell to a shock 4-3 defeat at the hands of Sassuolo, who climbed out of the Serie A relegation zone.
Riccardo Montolivo scored Milan's third four minutes from time, but it proved a mere consolation as Milan were drawn to within six points of the drop zone.
