Massimiliano Allegri made five changes to the side that drew 2-2 at Cesena last time out but his defending champions hinted that they might stumble again when Giulio Migliaccio headed the visitors to Juventus Stadium into a 25th-minute lead.
Fernando Llorente netted a scruffy equaliser six minutes before half-time before midfield maestro Pirlo took centre-stage on the stroke of the interval with a dazzling long-range effort.
Juventus pressed to make the game safe in the second period, Paul Pogba coming closest to extending their lead.
Clear chances dried up during the closing stages of a result that means second-place Roma will kick off 10 points in arrears when they travel to Verona on Sunday.
Atalanta have now lost three consecutive matches and remain precariously perched three points above the relegation zone.
Juventus penned their lowly opponents in their own territory during the opening stages and Llorente might have done better when he steered two Pirlo deliveries off target in the opening 10 minutes.
For all the home dominance, Gianluigi Buffon made the first telling save of the match, thwarting Daniele Baselli from close range.
From the resulting corner, Stefano Colantuono's team stunned the Turin faithful as Migliaccio darted towards the near post and glanced a header against the far upright that crossed the line before Buffon gathered.
Roberto Pereyra could have levelled immediately but an unnecessary touch on the end of Carlos Tevez's low cross allowed goalkeeper Marco Sportiello to smother his eventual shot.
In the 39th minute, Juventus full-back Martin Caceres stormed into the box and was denied by Sportiello. Again, a goalkeeper's good work would go unrewarded as Llorente smuggled home when the subsequent corner prompted an ungainly penalty box scramble.
If the equaliser was ugly, Juventus' second was simply beautiful - Pirlo launching a sumptuous 30-yard strike that swerved and dipped enough to leave Sportiello grasping at air.
The Atalanta keeper saved remarkably to keep out Pogba's close-range header in the 53rd minute.
A few moments after squaring up to Lionel Scaloni and earning a yellow card, Juventus midfielder Claudio Marchisio caught a boot in the face from Luca Cigarini but was not awarded a penalty.
Tevez saw an effort bravely blocked and Atalanta defender Andrea Masiello made an excellent last-ditch challenge to deny substitute Alvaro Morata in the 84th minute, while Migliaccio again timed his run superbly to hand Juventus a late scare as he headed wide.
Having returned to winning ways, Allegri's men now look towards games against Borussia Dortmund in the UEFA Champions League and Roma in Serie A that could prove to be defining moments in their season.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.