Wayne Rooney scored a superb backheel to ease the pressure on Louis van Gaal and end Manchester United's eight-match winless run.
Rooney moved ahead of Denis Law to become the second-highest goal scorer in United's history when he struck with the final goal in the 2-1 win over Swansea on Saturday.
Rooney's first league goal since October could not have come at a better time for his under-fire manager.
Van Gaal's team looked like going nine matches without a win when Gylfi Sigurdsson's header looped over David de Gea to equalise Anthony Martial's eighth United goal.
But luckily for the Dutchman, Rooney came to his rescue when he deftly flicked the ball past Lukasz Fabianski in the 77th minute.
Van Gaal, who lined his team up in a 3-4-2-1 formation, was hoping for a change in fortunes at the start of the new year, but for the most part, his team served up another dull display.
The 64-year-old will not care too much, however. Rooney's goal buys him more time to turn things around at Old Trafford and his team are now fifth in the league - just two points behind Tottenham.
There was no sign of any Jose Mourinho scarves outside Old Trafford before kick-off.
United's encouraging performance against Chelsea had restored a certain amount of confidence in Van Gaal, it seemed, but what followed in the opening 45 minutes was the same old drivel from the hosts.
Ander Herrera tricked his way into the box in the first minute, but Federico Fernandez put in a crucial block. Thereafter, United were dour.
Twenty-nine minutes had passed before the first shot on target arrived. Luckily for United, Wayne Routledge volleyed straight at De Gea.
United did not test Fabianski until the 33rd minute. In reality, it was not much of a test for the Swansea stopper. Juan Mata's quick thinking allowed him to find space in the box from Herrera's quick free-kick, but his shot dribbled into Fabianski's hands.
The home fans became annoyed at their team's performance and their complaints were understandable. With three at the back, United had an extra man in midfield, but they were slow to turn defence into attack. Groans were heard as United passed back and sideways with regularity.
It came as no surprise when there were a few boos from home fans when the half-time whistle went. It was the ninth successive game that United had failed to score in the first half at Old Trafford.
The home fans had their spirits lifted two minutes after the break. Ashley Young crossed to Martial, who powered a header in from eight yards. Van Gaal rose to his feet and held his arms aloft.
United almost threw their lead away when Andre Ayew was left unmarked in the box. The Ghanaian headed Sigurdsson's cross on to a post and the ball dropped to Angel Rangel, who went down as he jostled for the ball with Matteo Darmian. The travelling fans demanded a penalty, but Jon Moss booked Rangel instead.
Martial broke into the box twice, but failed to test Fabianski and United paid the price. Modou Barrow, given space down the left, crossed to find Sigurdsson, who looped a header over De Gea.
The home fans bemoaned another sloppy goal, but Rooney came to the rescue. After another pacy dribble down the left, Martial flashed the ball across the box and the United captain flicked the ball in.
Fabianski could have equalised in injury time when he came up for a corner, but he headed wide and United held on for a welcome win.
TWEET OF THE MATCH
@GaryLineker: "Delightful finish by Rooney. His record of scoring in every game this year is intact."
David De Gea: 7
Phil Jones (Darmian, 45): 5
Chris Smalling: 6
Daley Blind: 6
Morgan Schneiderlin: 6
Bastian Schweinsteiger: 6
Ander Herrera (Carrick, 90): 6
Ashley Young (McNair 78): 7
Anthony Martial: 7
Juan Mata: 7
Wayne Rooney: 7
Matteo Darmian: 5
Paddy McNair: 5
Michael Carrick: 5
Lukasz Fabianski: 6
Neil Taylor: 6
Ashley Williams: 6
Federico Fernandez: 6
Angel Rangel: 6
Jack Cork: 6
Leon Britton (Barrow, 62): 5
Ki Sung-yeung: 6
Wayne Routledge (Montero, 82): 6
Gylfi Sigurdsson: 7
Andre Ayew (Gomis, 82): 7
Modou Barrow: 6
Bafetimbi Gomis: 5
Jefferson Montero: 5
Anthony Martial again looked United's most potent goal threat. He came in from the left wing to head in the opener from Ashley Young's cross and then set up Wayne Rooney for the winner.
MOMENT OF THE MATCH
Old Trafford was preparing for more disappointment after Gylfi Sigurdsson headed Swansea level but Rooney came up with a touch of class for his first Premier League goal since October, expertly flicking in Martial's cross. His reaction was a mixture of delight and relief.
VIEW FROM THE BENCH
United boss Louis van Gaal opted for three at the back, with Phil Jones replacing Darmian in the starting line-up. Swansea caretaker Alan Curtis rotated his troops again, making seven changes from the 0-0 draw with Crystal Palace.
MOAN OF THE MATCH
There was a cautious optimism around Old Trafford after United produced a more expansive and fast-paced display against Chelsea last time out. But in the first half here they were back to plodding, safety-first football against a team who had won only one of their previous nine games. The second half was a distinct improvement and they got their rewards.
WHO'S UP NEXT?
Manchester United v Sheffield United (FA Cup, Saturday, January 9)
Oxford v Swansea (FA Cup, Sunday, January 10)