Arsenal rang in the new year by giving boss Mikel Arteta his first victory as lacklustre Manchester United crashed to a 2-0 defeat, while Tottenham and Chelsea also slipped up in the Premier League's top four race on Wednesday.

Arteta had watched Arsenal take only one point from his first two matches, with last weekend's 2-1 defeat against Chelsea especially painful after the Blues scored twice in the final minutes.

But Arsenal had played well for long periods in that London derby and they produced an even more sparkling display to put United to the sword at the Emirates Stadium.

The Gunners took the lead in the eighth minute when Sead Kolasinac's cross ran through to Nicolas Pepe at the far post and the Ivory Coast winger beat David De Gea from close-range.

Arsenal, who last won in the league at West Ham on December 9, got a deserved second goal in the 43rd minute when De Gea kept out Alexandre Lacazette's flick and Sokratis reacted quickest to lash home.

Arteta's team are nine points adrift of the top four, but their second win in 16 matches in all competitions offers hope of a brighter future under the former Arsenal midfielder's management.

United are fifth, five points behind fourth placed Chelsea, after the latest in a long list of underwhelming performances in a troubled campaign.

Tottenham and Chelsea slipped up in the Premier League's top-four race on Wednesday as David Moyes made an immediate impact on his return to West Ham during a busy programme of New Year's Day football.

Chelsea remain in pole position to secure the fourth Champions League qualification place but manager Frank Lampard will rue conceding a spectacular late equaliser in the 1-1 draw at Brighton.

Those dropped points gave Jose Mourinho's Spurs the chance to crank up the pressure on Chelsea and Manchester United but they slipped to a 1-0 defeat at Southampton and England captain Harry Kane limped off with a hamstring injury.

Elsewhere at the top of the table, second-placed Leicester cruised to a 3-0 win at Newcastle and Manchester City beat Everton 2-1 to hand Carlo Ancelotti his first defeat since taking over as manager.

Earlier on Wednesday, Cesar Azpilicueta gave Chelsea the lead on England's south coast, tapping in from close range in the 10th minute.

But Brighton scored the goal their persistence deserved in the 84th minute when Iranian substitute Alireza Jahanbakhsh acrobatically found the bottom-left corner with an overhead kick to give his team a share of the points.

"It was frustrating for different reasons," Lampard told BT Sport. "In the first half, the game was there to be won. We weren't ruthless enough. We got the goal and we had the possession. But we just didn't kill the game off.

"We allowed them to stay in the game. In the end it was a wonder goal but we were lucky not to lose the game."

The Chelsea boss said he was concerned about the lack of consistency from his side, who have beaten Tottenham and Arsenal in recent weeks but also lost at home to Southampton.

Tottenham travelled to in-form Southampton with the chance to overtake Manchester United and move three points behind Chelsea but they fell behind to a 17th-minute Danny Ings goal.

Mourinho's men were laboured in attack. Kane injured himself as he converted Christian Eriksen's free-kick in the second half but was flagged offside before hobbling down the tunnel.

Mourinho's frustration boiled over as he was shown a yellow card after an altercation with the Southampton bench.

"I was rude," the Spurs boss told the BBC. "I clearly deserved the yellow card. I had bad words."

"The work is not about buying, it is about working with the players on the pitch," he added. "It is something that is very difficult for us because we have no time to do it."

Ralph Hasenhuettl's Southampton are now in mid-table after a dramatic upturn in form.

Leicester appear to have put a mini-slump behind them, beating Newcastle 3-0 courtesy of goals from Ayoze Perez, James Maddison and Hamza Choudhury to move to within 10 points of leaders Liverpool.

Newcastle were forced to play almost the entire second half with just 10 men after Fabian Schaer was injured following all three substitutions.

Brendan Rodgers made six changes for the trip to the northeast and the win left his side 10 points behind runaway leaders Liverpool, having played two games more.

"It's not our concern to catch Liverpool," said the Leicester boss. "We get asked all the time but we are about developing the squad and the team."

Watford continued their impressive run under Pearson, holding on to beat seventh-placed Wolves 2-1 after a first-half goal from Gerard Deulofeu and a second-half effort from Abdoulaye Doucoure despite later being reduced to 10 men.

Earlier, Villa beat Burnley 2-1 despite seeing a Jack Grealish goal controversially chalked off by VAR -- a result that lifted them out of the relegation zone.

Wesley put Villa ahead in the 27th minute and captain Grealish doubled his side's advantage four minutes before the break as his powerful effort found the top corner.

Chris Wood pulled a goal back for Burnley with 10 minutes to go but Villa held on to secure all three points.

"It was massive. We've only had one away win all season before this," Grealish told the BBC. "To come here, one of the hardest places in the league, it was well-deserved and well-needed."

City remain in third after their home win against Everton, a single point behind Leicester.

Gabriel Jesus scored twice in the second half at the Etihad before Richarlison pulled a goal back for Everton but City held on despite some nervy moments.

"We played great so I am delighted for the guys," City manager Pep Guardiola told BT Sport. "This period is so tough. We did really well. Three more points and closer to Leicester.

"When you are far away from the first position sometimes people give up, but we never give up. We have to keep going. We have FA Cup then the (League) Cup. Other teams dropped points for the top four so it was an important win."

Struggling West Ham made a flying start under Moyes, returning to the London Stadium for a second stint as manager, hammering hapless Bournemouth 4-0 and lifting themselves out of the relegation zone, with the visitors now in the bottom three.

Mark Noble scored either side of a Sebastien Haller effort and Felipe Anderson bagged the fourth midway through the second half to complete the rout.

"The players were magnificent from the start, they bought into the idea to get the supporters back onside and they did," Moyes told the BBC. "I think it was a fabulous performance and fabulous result."