Higuain cancelled out Robin Gosens’ opener for Atalanta in the 74th minute before completing the turnaround with a second eight minutes later.
Paulo Dybala then sealed the points for Maurizio Sarri’s side in injury time.
Sarri’s side are four points clear of Antonio Conte’s Inter Milan, who face Torino later on Saturday (19:45 GMT).
Musa Barrow missed a first-half penalty for Atalanta, awarded following a handball by Sami Khedira, and Juventus keeper Wojciech Szczesny was forced into a good save by Mario Pasalic as the hosts threatened.
Gosens eventually headed Atalanta ahead from Barrow’s cross after 56 minutes, but Higuain’s deflected goal sparked Juventus into life.
The Argentine made no mistake when picked out by Juan Cuadrado eight minutes from time, and Higuain turned provider as Dybala weaved through the hosts’ defence for his side’s third.