Cuadrado struck direct from a corner that sailed over the head of Genoa goalkeeper Salvatore Sirigu within the ninth minute, with Dybala drilling a 2d past due directly to send Juve as much as 5th vicinity.
The victory begins an vital month for Massimiliano Allegri's side who will wish a run of beneficial furniture can allow them to shut the seven-point gap to the Champions League places.
Juve are 11 factors adrift of leaders AC Milan beforehand of fits in opposition to Venezia, Bologna and Cagliari inside the run up to Christmas and the iciness damage.
"We realize we need to carry on like this, to try and get to the final recreation in December with as many wins as viable to get toward the teams above," Dybala told DAZN.
Genoa have gained once in 16 video games this term, picking up simply one factor in 4 outings because the appointment of former Ukraine and Milan star Shevchenko.
They haven't begun to score underneath the 2004 Ballon d'Or winner and did now not try a single shot against Juve.
The league's joint-top scorer Dusan Vlahovic scored the winner from the penalty spot in a 3-2 victory at Bologna to go away Fiorentina degree on points with Juve.
Vlahovic's 13th aim of the marketing campaign moved the Tuscany side in advance of Jose Mourinho's Roma who lost 3-0 at home to champions Inter Milan on Saturday.
Vincenzo Italiano's Fiorentina ended a run of four consecutive defeats on the road to Venezia, Lazio, Juventus and Empoli.
Fiorentina's Youssef Maleh opened the scoring with a header after 1/2 an hour at the Stadio Dall'Ara for his first Serie A goal.
