De Gea stars in United's 6th successive win
The Spaniard pulled off a succession of important saves, mainly from Raheem Sterling in the first half.
LONDON - The difference in fortunes since Liverpool won 3-0 away to Manchester United in March was illustrated when Louis Van Gaal's team reversed that scoreline on Sunday.
Nine months ago the Merseysiders were challenging strongly for the Premier League title and United, having their worst season for many years, would shortly sack manager David Moyes.
After a slow start to the campaign United appear to have been revitalised by Van Gaal and goals from Wayne Rooney, Juan Mata and Robin van Persie sealed a sixth consecutive league win to keep them in third place.
Liverpool are languishing in mid-table, dropping to 10th after Tottenham Hotspur climbed above them with a 2-1 victory at Swansea City in the day's other fixture.
That said, it was a flattering margin for United, with many observers making United's keeper David De Gea man of the match.
The Spaniard pulled off a succession of important saves, mainly from Raheem Sterling in the first half and substitute Mario Balotelli in the second.
It was a typically feisty contest between the old rivals, ending with seven yellow cards, four to United before halftime.
Other statistics showed Liverpool had more shots and corners as well as plenty of possession but crucially they could not convert their chances, and made mistakes in conceding each goal.
Liverpool could claim luck was against them, with the second goal clearly offside but as manager Brendan Rodgers admitted they contributed to their own downfall.
"We created enough chances to win but we made defensive mistakes, which is what cost us," he told Sky Sports.
"I thought we did enough to win the game. But you can't concede the goals we did."
For the first one in the 13th minute, Joe Allen allowed Antonio Valencia to push the ball through his legs and had no cover behind him as the Ecuadorean played a square pass for Rooney to beat goalkeeper Brad Jones with ease.
Australian Jones was brought in as replacement for Simon Mignolet to start his first Premier League game since March 2013, but he was beaten again five minutes before half-time.
As Ashley Young cut back to cross, Mata was not offside but he was by the time Van Persie flicked the ball on.
Rodgers sent on Balotelli for Adam Lallana at the interval and Liverpool continued to see plenty of the ball.
Sterling should have scored five minutes into the second half after latching onto Jonny Evans's weak back pass but, one-on-one with De Gea, he allowed the keeper to deny him.
The young England international did better midway through the second half in setting up Balotelli, but De Gea pushed the Italian's shot onto the crossbar.
United's third goal stemmed from a classic counter-attack but was still helped by bad defending.
Mata sent Rooney away and Dejan Lovren should have cleared his cross. Off-balance, he skewed it straight to Mata, whose perfect pass was drilled in by Van Persie for a seventh league goal of the season.
There was still time for De Gea to make two more quality saves from Balotelli.
Van Gaal said that his goalkeeper "had a big influence" but was also critical of United for the number of chances they allowed the opposition. "We have to improve that," he told reporters. "We are winning now, six matches in a row is fantastic, but we still have to improve our playing style."
Tottenham's 2-1 away to Swansea moved them into seventh position, two places above the Welsh club.
Harry Kane headed Spurs in front in the fourth minute, Wilfried Bony equalised early in the second half with his eighth goal in the last 10 games but Christian Eriksen scored the winner just before the end.