Both teams scored twice in the opening 45 minutes, but Pique's close-range finish early in the second period proved enough for Barcelona to shade the entertaining pre-season friendly in the International Champions Cup.
Real Madrid captain Sergio Ramos featured for the first time this summer, while there were also starts for Mateo Kovacic and Marco Asensio as Zinedine Zidane, who was without the injured Toni Kroos, shuffled his pack for the pre-season clash.
As for Barcelona, Neymar was once again included in the XI despite the constant speculation surrounding his future. The Brazilian was joined in the final third by Luis Suarez and Lionel Messi, while Aleix Vidal and Jordi Alba were selected in the two full-back positions.
It took Barcelona just three minutes to make the breakthrough on the night, with Messi driving into the Real Madrid box before finding the back of the net courtesy of a big deflection off Raphael Varane, which saw the ball loop over the helpless Keylor Navas.
Barcelona were rampant in the early exchanges, and Ernesto Valverde's side doubled their lead in the seventh minute when Ivan Rakitic sent a low effort into the bottom corner after meeting a loose ball on the edge of the box.
It might have been 3-0 in the 11th minute when Luis Suarez fed Rakitic, but the Croatian missed the post with a low strike, before the former smashed the ball over the crossbar after meeting a clever free kick from Messi.
Real Madrid were back in the match in the 14th minute, however, when Kovacic found a yard of space just outside the Barcelona box after smart work from Casemiro before arrowing the ball into the far corner of the net.
Benzema then came within a few inches of levelling in the 20th minute when the Frenchman drove to the edge of the area before releasing a powerful strike, only to see the ball move the wrong side of the post.
The fixture was friendly in name but certainly not in nature as late challenges continued to arrive, and Real Madrid centre-back Varane picked up a yellow card in the 22nd minute for chopping Neymar to the ground.
Neymar had a glorious chance to send Barcelona 3-1 ahead just before the 30-minute mark after turning Varane inside the Real Madrid box, but the Brazilian's low effort just missed the far post, before Messi brought a smart save from Navas moments later.
Real Madrid were always a threat on the counter-attack, however, and Zidane's team levelled the scores via that avenue in the 36th minute when Asensio found the bottom corner from inside the Barcelona box after collecting an incisive pass from Kovacic.
Jesus Vallejo was among three players to come off the Real Madrid bench at the interval, but Barcelona boss Valverde made just the one half-time alteration - Sergi Roberto taking the place of Andres Iniesta.
The tempo remained high at the start of the second period, and Barcelona regained the lead in the 50th minute when Pique turned a clever Neymar free kick past Navas from inside the six-yard box.
Neymar had a wonderful chance to send Barcelona 4-2 ahead in the 55th minute after rounding Navas inside the Real Madrid box, but the Paris Saint-Germain transfer target somehow sent his effort wide of the post.
Marcelo was down the other end moments later as Real Madrid looked to level, but the Brazilian full-back could not find a route past Barcelona goalkeeper Jasper Cillessen as Valverde's side remained 3-2 ahead at the Hard Rock Stadium.
An end-to-end period of the match continued to produce opportunities, and Barcelona centre-back Umtiti had a goal-bound strike cleared off the line, before Isco brought a really smart save from Cillessen down the other end of the field.
Neymar was among those to leave the field in the 72nd minute as both managers looked to their bench for the final stages of the contest, while Dani Ceballos, Theo Hernandez and Marcos Llorente all came off the Real Madrid bench.
Cillessen made another outstanding save to tip an Isco strike wide of the post 10 minutes from time, before Ceballos just missed the bottom corner with a rasping strike in the 84th minute as Barcelona remained ahead.
Both teams had bright moments in the latter stages as a number of youngsters looked to impress, but 3-2 was how it finished on the night as Barcelona won the first ever El Clasico in North America.
Next up for Real Madrid is a clash with MLS All-Stars on Wednesday as their pre-season tour of the United States comes to a close, while Barcelona will now return to Spain as they prepare to face Brazilian outfit Chapecoense in the Joan Gamper Trophy on August 7.