United struck early, with Matheus Cunha firing home from outside the box in the sixth minute before Benjamin Sesko doubled the advantage in the 14th minute following a goalmouth scramble.
With momentum swinging in Liverpool’s favour, United regained control late on when Kobbie Mainoo struck from the edge of the box in the 77th minute, drilling a low shot into the bottom corner to restore the lead.
Despite late pressure from Liverpool, including attempts from Federico Chiesa and Cody Gakpo, United held firm to secure all three points in front of a crowd of 74,027.
The closing moments saw Diogo Dalot miss a clear chance to extend United’s lead, but it proved inconsequential as the final whistle confirmed a hard-fought victory for the hosts.