The Old Trafford fans showed their faith in much-maligned Manchester United manager David Moyes by unfurling a banner supporting the boss - but the first half was staggeringly drab as United's players failed to look like they’d met each other before the game, and Swansea seemed keener on retaining possession than scoring.
Adnan Januzaj went close, clipping the bar with a free kick. Patrice Evra also dragged a shot across goal for Gerhard Tremmel to stop easily, and Welbeck pulled a snap-shot wide of goal from a Rafael pass.
Swansea saw plenty of the ball, but their best chance was Jonjo Shelvey’s poor shot when he had space just inside the box shortly before half-time.
In the second period, however, the home fans' faith in Moyes was repaid: Valencia broke the deadlock moments just two minutes after the restart when he turned in a Shinji Kagawa header that was palmed away by Tremmel.
And on 59 minutes, Welbeck doubled United’s lead, flicking Patrice Evra’s shot goalwards.
Chris Smalling should have made it three as he blazed a simple effort over the bar from almost point-blank range, while later in the match Kagawa was put through in a one-on-one with the ‘keeper.
Kagawa contrived to trip and waste the chance - but the points were already secure, and Moyes will be relieved to have broken the run of bad results which had piled pressure on him and his team.
11’ - JANUZAJ FREE KICK - The winger clips the bar with a set-piece just outside the box.
28’ - EVRA SHOT - A moment of time for the full-back on the edge of the area, but his shot is saved by Tremmel.
36’ - WELBECK MISS - After good work from Valencia to Rafael, the Brazilian sends a pass for Welbeck to fire wide of goal.
39’ - SHELVEY SHOT - Amat plays the ball wide to tee up Shelvey, who drags his shot wide.
47’ - VALENCIA GOAL - Januzaj curls in a cross, and Kagawa heads towards goal at the back post. Tremmel saves but Valencia is on hand to turn the ball into the goal.
59’ - WELBECK GOAL - Evra pokes a shot towards goal after a cross from Januzaj is headed out, and Welbeck flicks the ball into the goal.
67’ - SMALLING MISS - Kagawa curls in a cross from the left, and with the goal gaping Smalling sends his shot over the bar from two yards.
76’ - KAGAWA MISS - Rafael produces a seventy yard sprint, lays the ball off for Shinji Kagawa, who beats one defender, trips, sends the ball past the keeper and has his weak shot cleared off the line.
Manchester United have now won five of their six Premier League meetings with Swansea City.
Swansea City have only won one of their last eight Premier League away games (D2 L5).
Nemanja Vidic made his 200th Premier League appearance in this match.
This was the first match against United that Wilfried Bony failed to score in this season.
Is Michael Carrick finished? Unfairly maligned for the past two years, it now seems all the criticism of the past is valid. Ponderous, unable to perform as an inspiring senior member of the squad, he might not need a partner to be bought as much as a replacement.
MAN OF THE MATCH
Adnan Januzaj (Manchester United): Once swapped to the wing, he teamed up with Shinji Kagawa to show what happens when good players play in their best position - they play well. Without him United would not have won, and without him they would be in a desperate position for the rest of the season.
Manchester United: De Gea 6, Rafael 7, Smalling 6, Vidic 6, Evra 6, Valencia 6, Carrick 5, Fletcher 6, Januzaj 8, Kagawa 7, Welbeck 7. Subs: Büttner 6, Hernandez 6.
Swansea City: Tremmel 6, Rangel 6, Amat 6, Williams 6, Davies 5, Britton 6, Canas 6, Shelvey 7, Pozuelo 6, Routledge 6, Bony 6. Subs: Chico 6, Vazquez 6.
THE MATCH IN A TWEET