Kai Havertz scored Arsenal's goal in front of a crowd of 69,879 at the home stadium of the NFL's Philadelphia Eagles.
In other friendly action in the United States, Chelsea swept past Mexico's Club America 3-0, AC Milan beat Real Madrid 1-0 and Manchester United edged Real Betis 3-2.
Egyptian Salah opened the scoring for Liverpool in the 13th minute, outpacing the defenders to latch onto Harvey Elliott's defence-splitting pass.
The striker shrugged off the attentions of Arsenal centre-back Gabriel and fired a low left-footed shot past Arsenal goalkeeper Karl Hein.
Carvalho doubled Liverpool's lead in the 34th minute, with Elliott again the provider.
The Portuguese winger ran onto a perfectly lofted Elliott pass into the box and fired home a crisp right-foot volley through Hein's legs.
Arsenal reduced the deficit in the 40th minute when Havertz scored past Liverpool goalkeeper Caoimhin Kelleher from point-blank range after Martin Odegaard found him in the six-yard box.
A goalless second half secured the triumph for Liverpool's new Dutch manager Arne Slot, who has replaced Jurgen Klopp.
Arsenal's newly signed 22-year-old Italian defender Riccardo Calafiori was not in the Gunners' lineup.
At San Diego, Real Betis grabbed an early advantage thanks to Iker Losada's strike in the 15th minute.
The lead lasted only three minutes as Romain Perraud fouled Manchester United's Amad Diallo in the box and Marcus Rashford blasted home from the spot.
Diallo gave the Old Trafford club the lead in the 24th minute and Casemiro added a left-footed strike off a pass from Rashford in the 31st for a 3-1 half-time lead.
Diego Llorente's 61st-minute header pulled one back for Betis.
In Atlanta, Chelsea's French striker Christopher Nkunku converted a penalty in the third minute to set them on their way against their Mexican club opponents.
Spanish 18-year-old Marc Guiu scored the second with a 21st-minute header.
Winger Noni Madueke scored Chelsea's second penalty of the game in the 79th minute to seal the 3-0 win.
In Chicago, Nigerian international Samuel Chukwueze's 55th minute goal gave AC Milan a 1-0 victory over Real Madrid.
