Rooney was isolated for much of this game, feeding off scraps, but took his chance well with a true strike after Fellaini rattled the crossbar with a header.
Many global football fans mark this fixture as one of the games of the Premier League season -- the rivals have 38 league titles between them -- but the two powers have struggled this campaign.
They kicked off lying in ninth and sixth place in the standings, respectively, and the first half showed just why. There was plenty of energy and snappy tackles but little quality, especially from United.
The teams were involved in thrilling 3-3 draws in midweek. They went from feast to famine a few days later.
Liverpool carved out some openings, for Roberto Firmino, Jordan Henderson and James Milner, but De Gea wasn't tested once and the shots were from long range. At the other end, opposite goalkeeper Simon Mignolet was little more than a bystander.
De Gea stepped up for United in the second half, though. He saved with his feet a low shot from Can, who then brought a superb diving save out of the Spain international with a fierce drive.
In between those chances, Anthony Martial finally got in behind Liverpool's defence and flashed a left-foot shot just past the far post -- United's first genuine effort.
It meant Rooney's goal came against the run of play for United, which maybe made it even sweeter for the celebrating visiting fans, including injured United players Phil Jones, Marcos Rojo and Michael Carrick.
-AP