Mauro Icardi came of the bench to open the scoring for the Nerazzurri late in the game, but Arturo Vidal salvaged a point for the Bianconeri
Both sides had their moments throughout the Serie A encounter, but it looked like the hosts had done enough to earn all three points when substitute Mauro Icardi opened the scoring in the 73rd minute.
However, the champions responded immediately as Arturo Vidal equalised just two minutes later to ensure both teams remain unbeaten after three top-flight fixtures.
Inter went into the clash high on confidence after beginning the campaign with two wins from two games, the latest coming at Catania prior to the international break.
Nerazzurri trainer Walter Mazzarri made just one change to that team, with Saphir Taider replacing Mateo Kovacic.
Juventus also started the season with consecutive victories and, in his 100th match in charge, coach Antonio Conte choose Carlos Tevez to once again partner Mirko Vucinic in attack as Fernando Llorente settled for a place on the bench.
The match started at a ferocious pace in the opening quarter of an hour and Inter created the first chance on goal as Yuto Nagatomo struck a volley from inside the penalty area after Alvarez's corner, but Gianluigi Buffon got down to his right to palm away.
Juventus looked dangerous when they were able to get into attacking positions, and the champions thought Vidal had won a penalty when he went down under pressure from Taider, but the Chilean was instead booked for diving.
Inter's productivity in attack increased as the first half went on, but it was Pogba who should have opened the scoring for the visitors just after the half-hour mark.
However, the France international's close-range effort after Andrea Pirlo’s lofted pass was saved Samir Handanovic.
The first period ended with Mazzarri's side on the front foot, but Buffon was in good form to deny Taider after the Algerian skipped past Stephan Lichtsteiner down the left and shot from a narrow angle.
The first 10 minutes of the second half proved to be cagey as neither side posed much of an attacking threat and Juventus appeared increasingly content to sit back and absorb pressure from the hosts.
However, Conte's men still looked dangerous on the counter-attack and they almost broke to devastating effect just before the hour.
Tevez cut in from the right before playing Vidal in, but he could only fire wide of Handanovic's left-hand post.
But the deadlock was eventually broken at the other end 17 minutes from time as Icardi - who had been introduced from the bench just six minutes earlier - latched on to a perfect through-ball from Ricky Alvarez and fired first time past Buffon.
However, Juventus managed to hit back straight away as Kwadwo Asamoah muscled his way past two defenders down the left before hitting a low cross into the danger area, which Vidal controlled with a superb first touch before placing the ball into the bottom corner.