Paulo Dybala Celebrates Goal
Argentina forward Dybala slotted home his spot-kick with a minute left after Denzel Dumfries was ruled to have kicked Alex Sandro, a decision that enraged Inter to the point that coach Simone Inzaghi was sent off by referee Maurizio Mariani.
Juve are up to sixth on 15 points, level with Atalanta and Fiorentina, while champions Inter stay seven points behind Napoli and city rivals AC Milan in the title race.
Inter thought they had won the match thanks to a goal from Edin Dzeko, who rolled into an empty net in the 17th minute after Hakan Calhanoglu's rocket of a shot rebounded to him off the crossbar.
It was another important goal from Dzeko, who also starred in Inter's 3-1 Champions League win over Sheriff Tiraspol midweek and has quickly become a fan favourite at the San Siro after arriving from Roma in the summer.
Juve were fortunate to get a point, not only because of the way the penalty came about but because of another underwhelming display.
Massimiliano Allegri's side offered little in the way of goal threat even after the introduction of Federico Chiesa and Dybala just after the hour mark.
Inter meanwhile were livid at being denied a win in what is traditionally their biggest domestic home match of the season thanks to what they saw as a very soft penalty.
Napoli's winning streak ended at eight games following their draw at the Stadio Olimpico, which also means Roma keep the record for the most wins from the start of a Serie A season, with 10 consecutive victories in 2013/14.
Both sides will be ruing missed chances which could have decided a tight, at times poorly tempered match between two rivals in which both coaches were sent off.
Roma boss Jose Mourinho was sent to the stands for dissent with nine minutes left while an incredulous Luciano Spalletti was shown a red card after the final whistle for what referee Davide Massa thought was sarcastic applause.
It was a decent result for Roma, who needed a good showing following their 6-1 humiliation at the hands of Norwegian outfit Bodo/Glimt in midweek.
"It's a good point, we came here knowing Roma wanted to react after Thursday's defeat and had their fans behind them," Koulibaly said to DAZN.
"The important thing was not conceding because we know that we can score at any moment. Not everyone can come here and keep a clean sheet."