Quick-fire goals from Wayne Rooney and Juan Mata in the second half cancelled out Steven Gerrard's opener as United claimed early bragging rights over their Premier League rivals.
Substitute Jesse Lingard completed the scoring with a fine volley from the edge of the area in the 89th minute at Sun Life Stadium in Miami.
Rooney - named captain for the fixture - put United on level terms in the 55th minute before Mata completed the turnaround with a goal of his own just two minutes later as Louis van Gaal's team ended their tour of the United States unbeaten.
United were forced to make one change to the team that started against Real Madrid, with Javier Hernandez replacing the injured Danny Welbeck in attack for the club's final match in the United States.
United made a composed start in Miami and were unfortunate not to take a fifth-minute lead as Sakho was on hand to scramble the ball clear ahead of the onrushing Mata following Ashley Young's teasing cross into the six-yard box.
Liverpool began to cause problems and Brendan Rodgers' men were awarded a penalty in the 14th minute after United defender Phil Jones fouled Raheem Sterling.
But whatever Van Gaal said during his half-time team talk worked as United restored parity 10 minutes into the second half courtesy of Rooney, who was on the end of Hernandez's cross to side-foot the ball into the far corner of the net - his fifth goal on tour.
It got better for United two minutes later when Mata beat goalkeeper Simon Mignolet from the edge of the area, albeit with a deflection off Sakho, before Lingard's fine finish late on.
