Miralem Pjanic flicked the ball to Higuain on the edge of the area and the Argentina worldwide fired a right-footed strike into the bottom left corner.
Adem Ljajic handed the visitors the lead after 52 minutes, before Gonzalo Higuain rescued the league leaders with the equaliser in stoppage time.
Juventus' incredible home Serie A winning streak of 33 matches was ended by Torino on Saturday in a hotly contested Turin derby, but it very almost could have been worse.
Napoli moved two points clear of Roma, who slipped into third, ahead of their match with AC Milan on Sunday.
"I could see from the touchline that he got the ball cleanly".
"We did something nobody else had been able to do, which was to stop Juventus winning at home in Serie A and we did it with 10 men".
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Three days before Juventus host Monaco looking to reach the Champions League final after their 2-0 first leg, semi-final win last week, coach Massimiliano Allegri called for composure.
Torino took a shock lead when Ljajic floated a flawless free kick over the wall and in off the underside of the crossbar, leaving Norberto Neto stranded.
Juventus spurned a slew of chances with Leonardo Bonucci smashing into the stands from six yards out, following Medhi Benatia's header hitting the crossbar.
"We're all happy. They all played well, more or less".
Despite Acquah's sending-off, Hart had only one hard save to make, from Leonardo Bonucci at close range, until Higuain struck with his 24th goal of the season.
Napoli forward Lorenzo Insigne, right, celebrates with his teammate Dries Mertens after scoring a goal during the Italian Serie A soccer match between Napoli and Cagliari, at the San Paolo stadium in Naples, Italy, Saturday, May 6, 2017.