Goals from Jadon Sancho and Marcus Rashford either side of half-time gave Man United and manager Erik ten Hag a massive three points despite it only being the third game of the season for both sides. Mohamed Salah scored late in the match for Liverpool, but the Red Devils hung on for the win.
As promised before the game, a large group of United fans angry at the direction of the club under American owners the Glazer family took part in a protest outside Old Trafford.
The hosts came in without a point from their first two matches, but at 16 minutes Sancho picked up a pass in the centre of the area from Anthony Elanga, composed himself and calmly shot past Alisson to give United the lead.
United defended well throughout the remainder of the first half, offering Liverpool few chances, and took a 1-0 lead into the break.
Rashford doubled the home side's advantage shortly after the restart with a lovely finish past Alisson from Anthony Martial's through ball that left him with only the keeper to beat.
The Old Trafford crowd roared on their team throughout the rest of the second half and Liverpool looked uncharacteristically out of answers as they sought to find a way back into the game.
Salah popped up to halve the deficit from close range in the 81st minute for Liverpool and set up a nervy finish to the game for United, but Jurgen Klopp's team couldn't find the equaliser and remain without a win this season.
There was plenty for Ten Hag to be encouraged by, particularly Rashford's return to scoring and form, but he will likely be delighted with the positive performances of two of his new signings.
Lisandro Martinez was outstanding in the centre of defence alongside the recalled Raphael Varane while Tyrell Malacia, picked ahead of Luke Shaw at left back, was tenacious throughout.
"We can talk about tactical but it is all about attitude. There was communication and a fighting spirit," Ten Hag said. "I wanted a different approach and a different attitude and that is what they brought on the pitch. It is only a start. We can play with much more composure and much more danger. Be a team, and have a good spirit and that is what we saw today."
The result lifted Ten Hag's side off the foot of the table into 14th place, while last season's second-place finishers Liverpool, whose Premier League streak of 21 games without a loss was snapped, are in 16th on just two points from their first three games.