The hosts, who have so far struggled to match the form that saw them finish fourth last time out, levelled up with 67 minutes played at the Atleti Azzurri d'Italia.
Juve so nearly maintained their perfect run late on, only for Paulo Dybala to miss from the penalty spot to see his side's winning streak in the Italian top flight end at eight games.
The Bianconeri got their breakthrough goal 21 minutes in, though, as Bernardeschi fired home his first goal for the club from close range after Berisha this time failed to deal with the initial shot.
Bernardeschi was involved in the second Juve goal, which arrived three minutes later when playing in Higuain to thump the ball home.
Defending champions Juve were surprisingly unable to see things through, however, with Mattia Caldara pulling one back on the half-hour mark after Gianluigi Buffon could only parry the ball into his path.
Medhi Benatia and Higuain both came close to restoring the visitors' two-goal lead, while a Mandzukic goal was discredited following a VAR review.
Atalanta were level 67 minutes in through a well-taken Bryan Cristante header, leaving Buffon rooted to his spot and Juve in need of a response.
The final big moment in the match came late on when, following a VAR review, Juventus were awarded a penalty which Dybala could not convert - Berisha pulling off one more big save to ensure that Napoli sit atop the Serie A pile.