Juventus ended Inter Milan's perfect record in Serie A and moved to the top as Gonzalo Higuain's superb late strike sealed win over their rival in the San Siro.
Paulo Dybala's opener was canceled out by a Lautaro Martinez penalty before Higuain's late decider ended Conte's unbeaten start in the league.
It took just four minutes for the visitors to break the deadlock. Miralem Pjanic's long pass found Dybala on the edge of the box and the Argentina international fired home past the outstretched arms of goalkeeper Samir Handanovic for the opener.
Five minutes later Cristiano Ronaldo came close to doubling his side's lead as his powerful effort from the edge of the 18-yard box struck the crossbar.
Inter pressed for an equalizer but Nicolo Barella fired over the bar following a corner, moments before they were awarded a penalty, confirmed by VAR after Matthijs De Ligt handled the ball in the area.
Martinez stepped up to take the resulting spot-kick and struck the ball powerfully into the bottom corner, leaving Wojciech Szczesny - who guessed the right way - with no chance after 18 minutes.
Ronaldo fired a free-kick at the Inter wall as Juve attempted to restore their lead midway through the first half, while Romelu Lukaku received medical attention over a knock for the hosts.
Inter came close to taking the lead as the half-hour approached but Szczesny pulled off a great save to deny Martinez at the far post.
The home side lost Stefano Sensi to injury after 33 minutes and to make matters worse, it looked like Juve had gone ahead for the second time just before the break before Ronaldo's strike was ruled offside.
The Bianconeri started the second half with intent and Federico Bernardeschi came close with a long-range effort before Ronaldo pelted Alex Sandro's pass well wide of the upright.
Dybala went in search of a second goal and had a great chance when one-on-one with Handanovic, but the Slovenian stopper did enough to deny him after 56 minutes.
Juve were denied a penalty shout on the stroke of half-time and the Nerazzurri had an appeal turned down themselves as Lukaku was brought down by De Ligt midway through the second half.
Inter midfielder Marcelo Brozovic hit a post minutes later and - at the other end - Ronaldo forced Handanovic to save his low angled shot with his legs as both sides pressed.
The visitors took the lead for the second time with 10 minutes remaining as second-half substitute Higuain picked up Ronaldo's pass in the box and made no mistake, firing the ball beyond Handanovic.
The home side surged forward and Brozovic came close to equalizing but he was denied by a vital save from Szczesny before Matteo Politano's corner found the goalkeeper's hands as Juve held on.
Juventus entertains Bologna on October 19 after the international break, while Inter has an away trip to face Sassuolo the following day.