Rather than attempting to build on their momentum, however, Simone Inzaghi's side retreated and dropped increasingly deep after the restart in a bid to protect their lead.
The introduction of Chiesa and Dybala off the bench after 65 minutes gave Juventus fresh impetus, and Massimiliano Allegri's decision paid dividends when Alex Sandro was awarded a controversial penalty, given after the referee re-watched the incident on the pitch-side monitor.
Inzaghi was sent off for his protestations and Dybala held his nerve to send Handanovic the wrong way and ensure the Old Lady shared the spoils.
The draw leaves Inter seven points adrift of the leaders Napoli in third, while Juventus are three points further behind in sixth.
After a dominant first half display, it appeared the Nerazzurri had their great rivals exactly where they wanted them. With Dybala and Chiesa starting on the bench, Juventus had offered little in attack, while Inter were overrunning them in midfield.
But Inzaghi's decision to drop his defensive line significantly - to abandon any notion of playing attacking football and ultimately try to protect a slender lead for such a long period - appears to have cost his side three much-needed points. The Inter boss will be livid about the referee's decision to award a penalty, but Inter would arguably have had the game killed off by then had he been a little braver with his tactics.
After a largely insipid performance, Allegri will be delighted his Juventus were able to extend their unbeaten run to 10 games unbeaten in all competitions. It was far from a satisfactory performance, but considering the Old Lady were in the bottom three just a few short weeks ago, and they're now just a point behind the top-four places, the hierarchy will be pleased with the progress he's making.
Edin Dzeko of FC Internazionale celebrates after scoring their team's first goal during the Serie A match between FC Internazionale and Juventus at Stadio Giuseppe Meazza
Image credit: Getty Images
MAN OF THE MATCH - Nicolo Barella (Inter)
In front of the watching Italy boss Roberto Mancini, the 24-year-old produced a masterclass in midfield, demonstrating his beautiful close control, range of passing and his ability to drive his team forward.
17' - GOAL! Inter 1-0 Juventus (Edin Dzeko): Inter take the lead in the Derby d'Italia! Calhanoglu lets fly with a first-time screamer that crashes off the crossbar. Dzeko is perfectly positioned to meet the rebound, it's a difficult finish but he adjusts his feet well to make the finish!
87' - Penalty to Juventus! Dumfries catches Alex Sandro inside the penalty area and the referee wanders over to the monitor to have a look at the replay! That's not usually a good sign... and he's given Juve a late, late penalty! Inter boss Inzaghi is sent off for his complaints!
89 ' - GOAL! Inter 1-1 Juventus (Paulo Dybala, pen): Dybala sends Handanovic the wrong way as he slides the ball into the middle of the goal! Juventus may have rescued a point!
Paulo Dybala is the first Juventus player to score in three consecutive matches against Inter in Serie A in the three points per win era (since 1994/95).
Dybala has scored 18 of his 20 penalties taken in Serie A, including the last five.
Edin Dzeko has scored five goals in his first four home seasonal appearances in Serie A this season: in the three points per win era, only Mauro Icardi in 2017/18 and Marco Branca in 1995/96 have netted more with Inter after four games played at home (six goals).