Defeats by Tottenham Hotspur, Swansea and Sunderland had left United at risk of losing four successive games for the first time since 1961, but they blew off the cobwebs with an improved display at Old Trafford.

Antonio Valencia and Danny Welbeck claimed second-half goals to leave United four points outside the Premier League's top four in seventh place, six days after Swansea had dumped them out of the FA Cup on the same pitch.

"We started the game well, but we didn't do enough in the first half to get enough goals," United manager David Moyes told Sky Sports.

"Danny had a great chance to make it 1-0. We limited them to very few opportunities today. I can hardly remember any at all. In the end, we got the result we deserved."

He added: "We're hoping to give the supporters some more goals here -- not just the two. We'll maybe keep them for later on in the season."

Teenage winger Adnan Januzaj was the catalyst for United's victory and he went close to opening the scoring in the 11th minute with a free-kick that struck the crossbar.

Welbeck also squandered a glorious chance when he bundled wide, but the pressure told early in the second period when Valencia tapped home after Gerhard Tremmel parried a header from Shinji Kagawa.

Januzaj provided the cross for Kagawa and he was also the source of United's second goal, in the 59th minute, with a centre that was cleared to Patrice Evra, whose first-time shot was deftly flicked home by Welbeck.

Earlier, Eden Hazard and Fernando Torres scored two excellent goals as Chelsea won 2-0 at Hull City to climb to the top of the table.

Hazard, who turned 23 on Tuesday, broke the deadlock in the 56th minute at the KC Stadium, gathering a flick from Ashley Cole, evading a pair of defenders, and drilling a shot into the bottom-right corner.

Torres marked his 200th Premier League appearance with a late goal that saw him wriggle past Alex Bruce and slam the ball inside the left-hand post with his left foot.

Victory moved Jose Mourinho's side into first place above former leaders Arsenal, who visit Aston Villa on Monday, and set them up nicely for next weekend's home game with United.

Chelsea manager Mourinho dismissed French media reports linking man-of-the-match Hazard with a move to Paris Saint-Germain, saying: "The club doesn't want to sell him.

"Last year you saw a talented Hazard; this year he is a much more mature player. He deserves more than man of the match, probably player of the month. Not many are doing what he is doing."

Everton climbed back into the Champions League places with a 2-0 victory at home to Norwich City.

Gareth Barry put Everton ahead in the 23rd minute with a fine 20-yard shot that fizzed into the top-right corner, before Kevin Mirallas scored direct from a free-kick on the hour.

Tottenham Hotspur are a point behind Roberto Martinez's side in fifth place after beating Crystal Palace by the same score at White Hart Lane.

After Palace winger Jason Puncheon horribly miscued an early penalty, Christian Eriksen broke the deadlock in the 50th minute from Emmanuel Adebayor's flick-on.

A day after his transfer to Toronto FC was announced, Spurs striker Jermain Defoe was granted a warm reception after coming on as a second-half substitute and he claimed a well-taken goal with 18 minutes remaining.

"It was a typical Jermain Defoe finish," said Spurs manager Tim Sherwood.

"He's pounced on it and struck. I'll be sorry to lose Jermain. Toronto are getting a fine goalscorer."

Adam Johnson scored the first hat-trick of his professional career as Sunderland won 4-1 at Fulham to climb off the foot of the table and close to within a point of safety.

Johnson teed up Sunderland's other goal, for Ki Sung-yeung, with Steve Sidwell replying for the hosts.

West Ham United spoilt Ole Gunnar Solskjaer's first home game as Cardiff City manager as goals from Carlton Cole and Mark Noble gave Sam Allardyce's side a 2-0 win that took them out of the bottom three at their hosts' expense.

Meanwhile, a 66th-minute strike from captain Adam Lallana earned Southampton a 1-0 win at home to West Bromwich Albion.