Substitute Caracciolo poked home five minutes from time after Alessandro Matri had twice given the Bianconeri the lead in an entertaining match.
Matri opened the scoring with a close-range finish after six minutes but skipper Marco Rossi headed Genoa level just after the half-hour mark.
The Italian striker swept the home side ahead again on 58 minutes before Caracciolo's late strike.
Fiorentina also drew 2-2 at home with Catania, a result that increases the pressure on Fiorentina coach Sinisa Mihajlovic.
Juventus coach Antonio Conte, who has won three and drawn four of his first seven games in charge, said his side needed to work harder to improve.
"It's disappointing to concede so late - we've lost two points," he told Sky Sport channel. "We tried to control the game but we need to be more attentive in the final stages.
"It might be better to have lost a couple of the draws and won a couple but we're still unbeaten."
Genoa coach Alberto Malesani applauded the teams for trying to attack after five goalless draws in Serie A last weekend.
"It's always been my philosophy to play the game in the right way," Malesani, whose side move up to 10th, said. "The boys tried their hearts out in an intimidating atmosphere. I do this job with passion and I want my sides to play football."
Juventus, whose new stadium is being monitored by local authorities for structural safety, played the now familiar high-tempo pressing game of Conte and were soon in front.
Matri, restored to the starting line-up, deflected in Claudio Marchisio's shot from the edge of the area, and he almost grabbed a second on 25 minutes but his angled shot was blocked by the legs of goalkeeper Sebastien Frey.
Genoa were far from overawed by the electric atmosphere and equalised when Rossi escaped the marking of Giorgio Chiellini before meeting Alexander Merkel's inch-perfect cross with a downward header into the far corner.
The mercurial Mirko Vucinic, who was outstanding in the 2-0 win over AC Milan in Juve's last home match, was having a quiet night and it was Genoa who came closest to taking the lead at the start of the second half when the impressive Merkel's back-heel shaved the post on 55 minutes.
Two minutes later the persistent Matri grabbed his second to restore Juve's lead, calmly side-footing home from 12 metres after Andrea Pirlo had sold the Rossoblu defence a dummy.
Merkel saw his powerful header from Rossi's cross bounce back off the crossbar but the home side paid the price for sitting back on their lead when Carraciolo nipped in front of Chiellini at the near post to poke home Juraj Kucka's header.
Earlier on Saturday, a late goal from Maxi Lopez helped Catania snatch a 2-2 draw against Fiorentina.
In a thrilling game in Florence, the Argentine striker fired home on 83 minutes to give the Sicilians a richly deserved point after brilliant Stevan Jovetic strikes had twice given the Viola the lead.
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