Nemanja Vidic, Wayne Rooney and Dimitar Berbatov scored for United, which was never pressured by Chelsea, which didn't have a clear-cut chance in the game.
First-year Chelsea manager Luiz Felipe Scolari scoffed at the notion that Chelsea's problems required an influx of talent on the winter transfer market.
"More players? I don't want more players," he said. "I have very good players. Either we got to the top with these players or I go down."
Chelsea is still second, four points behind Liverpool and even in games played, but it has not played against the other teams in the EPL's big four. It has earned just one point in four games with Manchester United, Liverpool and Arsenal and faces an FA Cup replay at Southend on Wednesday.
The presence of former Chelsea manager Jose Mourinho -- on hand to scout United for its Champions League match against his current team, Italian champion Inter Milan -- only added to the pressure on Scolari.
"Mourinho came here to watch Manchester United, that is normal," Scolari said. "Mourinho is an intelligent man. He didn't come here to tell me he loves me."