Wayne Rooney’s brilliant instinctive winner beat Swansea as Manchester United ended a run of eight games without a win.
The England striker flicked home Anthony Martial’s cross with 13 minutes to go to settle a close contest.
After a dour first half, Martial had headed United in front, before Gylfi Sigurdsson’s glancing effort set nerves on edge at Old Trafford.
Manchester United move up to fifth, two points behind Tottenham.
Swansea’s raids forward were rare, but they twice came close to a second equaliser in injury time.
First Ashley Williams brought a good save out of David de Gea before goalkeeper Lukasz Fabianski headed wide from a corner with almost the last touch of the game.
How the action unfolded at Old Trafford
Listen to 5 live commentary of Wayne Rooney’s winner
Win can be start of fantastic 2016 – Van Gaal.
Rooney’s touch of class changes mood
Swansea had won all three of their league meetings with Louis van Gaal’s Manchester United – including the Dutchman’s very first match in charge.
History seemed dangerously close to being repeated for the home fans when Sigurdsson – the matchwinner in Van Gaal’s United debut – steered home Modou Barrow’s cross with 20 minutes to go.
Rooney’s afternoon up to that point had been full of industry but short on inspiration. However, United’s captain improvised brilliantly to flick Martial’s cross round his standing leg and into the far corner past a rooted Fabianski for the winner.
As well as delivering three points for his team, the strike gave Rooney sole possession of second place on the all-time goalscoring lists of the Premier League – on 188, 72 behind Alan Shearer – and Manchester United – on 238, 11 behind Sir Bobby Charlton.
Width + crosses = goals
The home fans’ relief was palpable on the final whistle as Manchester United secured their first win since beating Watford away on 21 November.
However, the half-time whistle had mostly been greeted with a bemused silence after a toothless first-half performance.
The one consistent source of danger for the hosts was right-winger Ashley Young. His pace and trickery gave Neil Taylor a testing afternoon and his consistently accurate delivery into the box was rewarded when Martial met a cross with a powerful header just after half-time.
The winner also came from the flanks as Martial drifted wide to turn provider for Rooney.
Fabianski almost provides stunning climax
Since losing his first match in charge across the city at Etihad Stadium last month, caretaker boss Alan Curtis had overseen three successive clean sheets to keep Swansea clear of the relegation zone.
And having kept United at bay for large spells in a tight and tidy performance, their discipline was almost rewarded in extraordinary style when Fabianski climbed highest after coming up for the final corner of the match and sent a header just wide.
Man of the match – Ashley Young
Manchester United manager Louis van Gaal: “I am very happy for the players because they had to play under big pressure and now we have won. We are still near the top of the league and the gap is less. So that’s football.
“That’s a season. A season takes eight months or something like that and not one month.
“I think we played a very risky system against Swansea because they had a shape with four midfielders in a diamond.
“I hope this is a fantastic starting point for us in the New Year and we can continue against Sheffield United.”
Swansea caretaker boss Alan Curtis: “Funnily enough, Lukasz Fabianski had asked a couple of minutes earlier to go up for a similar situation. I told him to stay back. I wish I’d asked him to go up earlier.
“We had to get back into the game. We were comfortable with the midfield diamond when it was 0-0, but once we went behind, we had to change things, so we put two wingers on to get back into it.
“We grew into the game after that, and we were unlucky not to get something.”