Argentine forward Dybala curled in a perfect free-kick eight minutes before the break after Brescia’s Florian Aye was sent off for two yellow cards in quick succession.
Colombian Cuadrado tapped in the second from close range after a Blaise Matuidi cross with 15 minutes to go, as the champions bounced back from last weekend’s shock defeat at Hellas Verona.
Juventus move three points clear of Inter Milan, with third-placed Lazio third, four points adrift of the leaders, before hosting Antonio Conte’s title rivals in the Stadio Olimpico later Sunday.
Cristiano Ronaldo was rested for Sunday’s game in Turin, but veteran defender Giorgio Chiellini returned after a long injury layoff.
Captain Chiellini came on for the final 12 minutes over five-months after rupturing cruciate ligaments in the right knee.
Brescia goalkeeper Enrico Alfonso went off after just 10 minutes following a knock to the head, with substitute keeper Lorenzo Andrenacci pulling off some fine saves against the champions.
Andrenacci smothered a second Dybala effort on the line minutes after the opener with the Brescia ‘keeper also denying Gonzalo Higuain just after the break.
Dybala missed the chance for a second just before the final whistle, clipping the bar with Andrenacci beaten.
Brescia fell to their fifth defeat in seven games, as they sit second-last in the table.
Earlier Hellas Verona missed the chance to close in on fifth-placed Roma, who fell 2-1 at Atalanta on Saturday, with a goalless draw at Udinese.
Sixth-placed Verona extended their unbeaten run to nine games and occupy the final Europa League berth ahead of Parma on goal difference.
Parma got back winning at Sassuolo with Ivorian Gervinho scoring the only goal after 25 minutes.
Fiorentina, in 13th, crushed struggling Sampdoria 5-1 after consecutive defeats to Juventus and Atalanta.
Federico Chiesa and Dusan Vlahovic bagged a brace each with the Tuscany side’s first goal a gift from Sampdoria midfielder Morten Thorsby who turned into his own net after eight minutes in Genoa.
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