Luis Diaz struck twice before halftime, with Mohamed Salah striking early in the second-half to take the game away from United.
Casemiro was at the heart of United's issues in the first-half and was hooked at the break by manager Erik ten Hag.
The win sees the Liverpool join Manchester City at the top of the table as the only two teams with a 100 per cent record after the first three games of the season.
United, meanwhile, sit in 14th place after consecutive defeats to Liverpool and Brighton.
At halftime, former United captain Roy Keane barked: "Same old problems, leopards and spots.
"They look very open when they've been, sometimes it's just one or two passes. They got away with the first couple of this alone. Obviously there has been mistakes. Mistake from Casemiro, for all his experience, that's not a first time pass. It's not worth the risk.
"And of course, when they lose it, they're all over the place. A player can make a mistake, but they've got to right back. They're all over the place, and they've done this for the last couple of games.
"The mistake Casemiro makes for the second one, the first goal, he gives away. I definitely think he should take a touch and with that situation, for all his experiences, awareness, he's got to do it quickly.
"He must be aware of what's around him, and then in defence, after this United do, if the defenders back and the players back for the second mistake.
"But that's the world class pass from Salah to finish, but Casemiro, for that incident there, he's got to do it quickly for the first goal, I think he's got to take a touch."