Stefano Sturaro had another chance to equalise on the half-hour mark, but headed narrowly over from a Pereyra corner.
Two minutes before the break, Claudio Marchisio sent a volley wide of the left post.
Seven minutes after half time, Valter Birsa's shot from inside the six-yard box was stopped by Buffon.
Pereyra then hit the post from the edge of the box on the hour mark, and Paul Pogba could only put the rebound over the bar.
Hernanes was next to go for goal nine minutes later, but Bizzarri tipped the shot round the right post.
Juventus scored an equaliser with just six minutes to spare when Hernanes was pulled down in the area. Dybala stepped up and put the penalty into the top-right corner.