Laurent Koscielny's goal saw Arsenal pull two points clear of second-place Leicester City at the Premier League summit on Saturday, while Wayne Rooney scored a milestone winner for Manchester United.
Koscielny stabbed home a flick-on from France team-mate Olivier Giroud in the 72nd minute at a rain-lashed Emirates Stadium to earn a below-par Arsenal a 1-0 victory over Newcastle United.
Leicester drew 0-0 at home to Bournemouth and now have just a one-point lead over Manchester City, who produced a rousing comeback to win 2-1 at Watford via late goals by Yaya Toure and Sergio Aguero.
"We were not at our best, but we had to dig deep and we can do that when needed," said Arsenal manager Arsene Wenger. "It was about solidarity, tired legs and taking a chance from a set-piece.
"Over Christmas, in four games we took nine points, so we can look back and say we did 75 percent of our job as we lost at Southampton."
Arsenal were far from their best against Newcastle, with Georginio Wijnaldum drawing smart saves from home goalkeeper Petr Cech either side of half-time and Aleksandar Mitrovic volleying over from close range.
But with the home fans growing restless, Koscielny supplied the breakthrough, sneaking in behind Ayoze Perez to toe the ball past Rob Elliot after Giroud had got his head to a high ball.
Leicester have now gone three league games without winning or scoring after their stalemate against 10-man Bournemouth at the King Power Stadium.
Leicester striker Jamie Vardy hit the post in the first half, while Riyad Mahrez saw a penalty saved by Artur Boruc on the hour after Simon Francis had been sent off for a last-man foul on Vardy.
However, Leicester manager Claudio Ranieri was eager to underline the positives, pointing out that his side have now reached the 40-point mark usually required to avoid relegation.
"A draw is not OK, it is only one point, but it is OK as we have 40 points, which was the goal," said the Italian. "It's champagne for my players!"
Manchester City were heading for a seventh successive winless away game after Aleksandar Kolarov's 55th-minute own goal put them behind at Watford.
But Kolarov teed up Toure to volley in an adroit 82nd-minute equaliser and Aguero then headed in an 84th-minute winner from Bacary Sagna's cross as Manuel Pellegrini's side reignited their title challenge.
"This team has a lot of character. We never give up," Pellegrini told Sky Sports.
"We are not sending messages. It was important to end those six away games without a win. We want to go game by game."
- Allardyce 'relief' -At Old Trafford, Rooney gave United a 2-1 win over Swansea City with a brilliant 77th-minute back-heel that made him the outright second-highest goal-scorer in both Premier League (188 goals) and United (238) history.
After Anthony Martial's header was cancelled out by Gylfi Sigurdsson, Martial teed up Rooney to score, ending United's eight-game winless run and further easing the pressure on manager Louis van Gaal.
"I am very happy for the players because they had to play under big pressure and now we have won," Van Gaal told the BBC.
"I hope this is a fantastic starting point for us in the New Year and we can continue against Sheffield United (in the FA Cup)."
The result lifted United to fifth place, two points below fourth-place Tottenham Hotspur, who visit Everton on Sunday.
West Ham United are a point back in sixth after Michail Antonio and Andy Carroll scored headed goals in a 2-0 home win over Liverpool.
Aston Villa spurned another chance to close on safety after losing 3-1 at second-bottom Sunderland, with Jermain Defoe scoring twice to leave Remi Garde's side seven points adrift at the foot of the table.
Patrick van Aanholt put Sunderland in front with a deflected effort and Villa were momentarily level courtesy of a superb Carles Gil volley in the 63rd minute before Defoe took centre-stage.
"It's a great relief," said Sunderland manager Sam Allardyce, whose side closed to within four points of safety.
"Hopefully it will give us confidence going forward. We're still very much in trouble, but this win was critical."
Jonny Evans's stoppage-time goal earned West Bromwich Albion a last-gasp 2-1 win over Stoke City, who had Geoff Cameron sent off after an altercation with Claudio Yacob.
Kenyan midfielder Victor Wanyama was dismissed as Southampton went down 1-0 at Norwich City, where Alexander Tettey scored a 76th-minute winner.