Argentina forward Dybala slotted home his spot-kick with a minute left after Denzel Dumfries was ruled to have kicked Alex Sandro as he tried to clear the ball, a decision that enraged Inter to the point that coach Simone Inzaghi was sent off by referee Maurizio Mariani.
His leveller came in his first appearance after a month out with a thigh injury, the 27-year-old coming on as a substitute in the 63rd minute.
"We were up against a very good team and given the way the game was going, we're happy with the point," Dybala said to DAZN.
Juve are up to sixth on 15 points, level with Atalanta and Fiorentina, while champions Inter are seven points behind Milan and Napoli (whose winning streak ended at eight games following their draw at the Stadio Olimpico).