Andreas Pereira's long-range free kick had cancelled out a penalty from Sadio Mane, but Daniel Sturridge, Sheyi Ojo and Xherdan Shaqiri netted in the second period to hand Liverpool the bragging rights in the pre-season clash.
United will continue their tour of the United States against European champions Real Madrid on Tuesday night, while Liverpool are back in action against Napoli next weekend.
Juan Mata had the ball in the back of the Liverpool net in the eighth minute of the match, but the offside flag was raised.
Jurgen Klopp's side almost took the lead moments later when Mohamed Salah flicked a header towards the United goal, but Lee Grant was on hand to make a wonderful save, before Ander Herrera cleared a Virgil van Dijk header off the line from the resulting corner.
Grant was again called into action to keep out another header from Salah in the 14th minute, before Mata had another goal disallowed in the 19th minute after finishing impressively from a Sanchez pass.
Liverpool were handed a penalty in the 27th minute when Demetri Mitchell kicked out at Salah inside the United box, and Mane dispatched the resulting spot kick to send the Merseyside outfit ahead.
United were level less than three minutes later, however, when Andreas Pereira, who has made a big impression for Jose Mourinho's side in the USA, sent a wonderful free kick into the top corner of the net.
Liverpool were the team pressing for a second as the first period approached its final moments, but the two rivals entered the half-time break at 1-1 following an entertaining opening 45 minutes of action.
Joel Pereira for Grant was United's only change at the break, but Liverpool boss Klopp made five changes, with Shaqiri entering the field for his debut.
Ojo headed towards the United goal just past the hour, although his effort never threatened to trouble Joel Pereira.
Liverpool did regain the lead in the 66th minute, however, when Sturridge slotted the ball into the bottom corner of the net with his first touch.
Fred came off the bench for his United debut in the 71st minute, but Liverpool had a third in the 74th minute when Ojo converted from the penalty spot after Herrera had clipped Andrew Robertson inside the box.
Alexis Sanchez had one deflected over the Liverpool crossbar 15 minutes from time as United looked to hit back, but the Merseysiders put the game beyond their rivals in the 82nd minute courtesy of an overhead kick from Shaqiri, which capped a miserable second half for the Red Devils.
MANCHESTER UNITED: Grant (J Pereira 46'); Darmian, Fosu-Mensah, Bailly, Tuanzebe (Williams 81'), Mitchell (Chong 71'); McTominay, Herrera (Gomes 81'), A Pereira, Mata (Fred 71'); Sanchez (Bohui 81')
LIVERPOOL: Grabara (Kelleher 46'); Camacho (Jones 65'), Klavan (Phillips 46'), Van Dijk (Gomez 65'), Moreno (Robertson 65'); Fabinho (Chirivella 65'), Lallana (Ojo 46'), Milner (Grujic 65'); Salah (Woodburn 46'), Solanke (Sturridge 65'), Mane (Shaqiri 46')