Cristiano Ronaldo scored with a long-range rocket on either side of Paulo Dybala and Douglas Costa's strikes before Andrea Pinnamonti pulled one back for Genoa.
Juventus remain in a strong position for a record-extending ninth straight Serie A title, the victory restored Juventus' four-point lead over Lazio, which won 2-1 at Torino earlier Tuesday.
Since losing the Italian Cup final to Napoli in a penalty shootout, Juventus have won all three of its league matches in the restart.
Dybala opened the scoring after the break by beating three defenders before unleashing a grass-cutter that Genoa keeper Mattia Perin, who is on loan from Juventus, could only get a weak hand on.
Seven minutes later, Ronaldo unleashed a blistering effort from 22 yards (meters) into the top corner past the outstretched Perin. Ronaldo has now scored 24 goals in 25 Serie A matches.
Substitute Douglas Costa made it 3-0 with a curling shot from beyond the area inside the far post as Genoa's defense looked on helplessly.
Andrea Pinamonti then pulled one back for Genoa from a tight angle.
The Immobile Show at Lazio
At Lazio, Ciro Immobile and Marco Parolo scored second-half goals to cancel out an early penalty from Andrea Belotti as Lazio beat Torino 2-1.
The win was, however, blighted by Immobile's yellow card which means that he will miss the crucial league tie against AC Milan on Saturday. The striker however atoned for his error with an expert finish to raise his total to 29 goals in 29 games - on pace to break Gonzalo Higuain's Serie A record of 36 goals in 2015-16.
Parolo scored the winner with a deflected shot from just beyond the area.
Torino is 14th, six points above the drop zone.
Serie A results
- Genoa 3-1 Juventus
- Lazio 2-1 Torino