The Brazilian forward, who has been strongly linked with Paris Saint-Germain in recent days, hit a first-half brace in the pre-season friendly in New Jersey, before Giorgio Chiellini hit back for Juventus in the second period.
Neymar and Lionel Messi both started in what was a strong Barcelona team, while there were also positions in the starting XI for Jasper Cillessen, Aleix Vidal, Paco Alcacer, Lucas Digne and Sergi Samper, but Luis Suarez was only among the substitutes.
The big news from the Juventus camp was that there was a first appearance for 20-year-old midfielder Rodrigo Bentancur, who joined the Italian champions from Boca Juniors earlier this summer.
Medhi Benatia was also included after completing a permanent transfer from Bayern Munich, while Mario Mandzukic led an attack which also included Mario Lemina and Stefano Sturaro. Douglas Costa, Gonzalo Higuain and Paulo Dybala, however, all started on the bench for the Italian champions.
Neymar twice found space down the left inside the opening couple of minutes, but the Brazilian could not take full advantage of his advanced position on the field.
Messi sent a free kick wide of Gianluigi Buffon's post in the ninth minute as Barcelona continued to press early on, before Manduzkic headed a searching Sturaro cross just wide down the other end of the field.
The game's opening goal was coming, and it was Barcelona that made the breakthrough in the 15th minute when Neymar collected a cute pass from Alcacer before sending the ball into the far corner of the net.
Neymar's first of the night was impressive, but his second was even better, with the Brazilian showing sensational footwork as he danced into the Juventus box in the 25th minute before sending a powerful effort past Buffon from close range.
Juventus had their moments in the first period, but it was Barcelona that continued to look the more likely to add to the scoring, with Messi forcing a brilliant save from Buffon just before the break after the Argentine had curled a free kick towards the top corner.
As expected, both managers made wholesale changes at the interval. Luis Suarez was among those to enter for Barcelona, while summer signing from Benfica Nelson Semedo was also introduced by new head coach Ernesto Valverde. As for Juventus, Wojciech Szczesny and Mattia de Sciglio were handed their debuts for the Italian champions.
Fellow substitute Miralem Pjanic might have halved the deficit in the 54th minute after smart work from Bentancur found the midfielder inside the Barcelona box, but his effort was into the stands, before Luis Suarez found Szczesny in decent form down the other end moments later.
Douglas Costa came on for his Juventus debut just before the hour, and the Brazilian was joined on the field by Juan Cuadrado, Higuain and Dybala as head coach Massimiliano Allegri freshened his attack.
Less than five minutes after Allegri had introduced some of his big-hitters, Juventus put their name on the scoresheet, with centre-back Chiellini heading home from close range after Barcelona goalkeeper Adrian Ortola had failed to make contact on a corner.
Barcelona should have scored a third in the 68th minute when Jordi Alba found Denis Suarez inside the Juventus box, but the Spain Under-21 international could only fire his effort into the stands, before Higuain ballooned one over the crossbar from close range down the other end seven minutes later.
Both teams had chances to register in what was an open finish to the entertaining pre-season friendly, but 2-1 was how it stayed as Barcelona started their preparations for the new campaign with a win.
Next up for Juventus is a clash with Paris Saint-Germain on Wednesday, while Barcelona will continue their pre-season against Jose Mourinho's Manchester United on the same night.