The Old Lady, seeking a fourth win from their first four games, were unable to build on their second-half lead as Inter hit back in style to prevent their opponents from claiming top spot.
Sami Khedira looked to be clean through inside the opening minute, only for the offside flag to go up on the far side to deny him a third goal of the season.
The Nerazzurri looked to move up a gear after seeing Khedira come close to a breakthrough, as Mauro Icardi curled one narrowly past the post just moments before Miralem Pjanic sent an attempt of his own wide at the other end.
Antonio Candreva saw a thunderous volley fizz inches past the target as the hosts continued to knock on the door, but it was Stephan Lichtsteiner who scored the opening goal when slamming home from close range.
Inter had to wait just two minutes for a leveller, though, as Icardi headed past Gianluigi Buffon, and things were about to get even better for Frank de Boer's side thanks to Ivan Perisic's back-post header 10 minutes later.
Gonzalo Higuain and Pjanic both had chances to earn Juventus a point at the home of their rivals but, despite seeing Inter reduced to 10 men late on when Ever Banega was shown a red card, the Old Lady could not find a way through for a second time.