With Ronaldo watching on at the Allianz Stadium as he served out a one-game ban after his red card against Valencia, Dybala helped the Serie A champion make it two wins from two in Group H.
His first was a wonderfully-timed volley from Leonardo Bonucci long pass, the centre-back's inch-perfect delivery dropping over the head of Mohamed Ali Camara to allow his team-mate to steer the ball in with his left foot.
His second was more about attacking instincts than technical ability, the forward tapping home the rebound after Young Boys goalkeeper David Von Ballmoos failed to steer Blaise Matuidi's stinging drive from the edge of the penalty area away from danger.
Dybala could have recorded a first-half treble had he made better contact with a first-time effort from Federico Bernardeschi’s cut-back cross, while a right-footed finish when through on goal soon after the break was kept out by a post.
However, his third eventually arrived in the 69th minute when he stretched out to poke home under pressure into an unguarded net, converting Juan Cuadrado's square pass from the right.
As well as conceding three goals for a second successive outing in the competition, Young Boys had to play out the closing stages a man down after defender Camara picked up two yellow cards in the space of three minutes.