This result left title-holders United 14 points adrift of leaders Arsenal with 16 league games of the season remaining and six off a place in the Champions League.

Their seventh league loss this term also turned the spotlight back on David Moyes, the successor chosen by Alex Ferguson, British football's most successful manager, to replace him following his retirement at the end of last season.

"We did not deserve to be 2-0 down at half time," Moyes told the BBC. "We had a little bit of bad luck with the first one (goal) but we can't blame anyone else but ourselves for the other two.

"We did not defend well enough and did not get a chance like Chelsea got to score, so we can only blame ourselves for that," the Scot added.

However, the former Everton manager insisted: "We will keep going. We showed a lot of good things today."

Victory left Jose Mourinho's Chelsea within two points of Arsenal.

"I think it is a big win and deserved, yes," Chelsea manager Jose Mourinho told the BBC. "They (United) started better than us, they had a good initiative.

"The second half was different. For 25-30 minutes we had very good control until we dropped back and they reacted with pride," explained the Portuguese boss after his 100th Premier League win as a manager.

"The second goal was the killer in the box I know from many years ago and it looks like Samuel Eto'o is coming back," added Mourinho, who managed the forward when they were both at Inter Milan.

Eto'o gave Chelsea a 17th minute lead when his shot from just outside the box deflected off Michael Carrick.

The 32-year-old veteran Cameroon striker made it 2-0 on the stroke of half time when, following Gary Cahill's centre, he smashed the ball home from six yards out.

United, without injured strikers Wayne Rooney and Robin van Persie, were 3-0 behind four minutes after the interval when more lax defending from a set-piece allowed Cahill a free header.

His effort was blocked by United goalkeeper David de Gea but, barely a yard away, Eto'o reacted first and made no mistake as he become the first Chelsea player to score a hat-trick against United since Seamus O'Connell in 1954.

Javier Hernandez, on as a substitute for Ashley Young, pulled a goal back 12 minutes from time.

But that was as good as it got for United whose misery was compounded when captain Nemanja Vidic was sent off in stoppage time for a rash challenge on Eden Hazard, with Rafael de Silva then fortunate to escape a red card for an equally wild lunge on Cahill.

"I have not seen Rafa's but I have seen Vidic's. Vidic's for me is not a red card, it was a yellow card," said Moyes. "If Rafa's was a bad one I would hopefully come out honestly and say what I think."

Earlier, Emmanuel Adebayor scored twice as Tottenham Hotspur moved level on points with Liverpool after a 3-1 win away to struggling Swansea.

Adebayor's goals, separated by a Chico Flores own-goal, ensured Tottenham remained unbeaten in the league under manager Tim Sherwood, whose record now stands at five wins and a draw since the Englishman replaced sacked predecessor Andre Villas-Boas.

After Swansea's Wilfried Bony had hit the crossbar, Adebayor gave Spurs the lead, against the run of play, in the 35th minute when he headed in an excellent cross from Christian Eriksen.

And the north London side made it 2-0 in the 53rd minute when Flores put Kyle Walker's cross into his own net.

Adebayor put the result beyond doubt 19 minutes from time before Bony scored a consolation goal.

Sherwood welcomed Adebayor's rediscovered hunger and form after the player became disillusioned and marginalised under Villas-Boas.

"It's obviously great for the football club and great for Ade himself, who's flying at the moment and enjoying his football."