Mikel Arteta’s first match as new Arsenal head coach ended in a 1-1 draw at Bournemouth.
Dan Gosling had put the Cherries in front after 34 minutes but Gunners captain Pierre-Emerick Aubameyang equalised just after the hour following a neat passing move.
Bournemouth forward Callum Wilson saw a goal ruled out for offside as both teams had to settle for a point.
New Everton boss Carlo Ancelotti, though, saw his reign get off to a winning start thanks to a 1-0 victory over Burnley at Goodison Park.
Dominic Calvert-Lewin finally broke the visitors’ resistance with 10 minutes left when his diving header to meet a cross from Djibril Sidibe went in off the post.
Elsewhere on Boxing Day, Southampton pulled further clear of the relegation zone with an impressive 2-0 win at Chelsea.
The Saints went ahead after 31 minutes when Michael Obafemi clipped the ball into the top corner from the edge of the penalty area.
Nathan Redmond made it 2-0 after 72 minutes with a close-range finish following a slick passing move as Chelsea were brought back down to earth after their win at Tottenham.
Aston Villa got the better of fellow relegation battlers Norwich with a 1-0 home win.
The Canaries saw a first-half header from Sam Byram hit the crossbar, while midfielder Alex Tettey later had a goalbound header cleared off the line.
But it was Villa who broke the deadlock in the 64th minute when substitute Conor Hourihane curled the ball into the top corner after good work from Jack Grealish.
Norwich pressed for an equaliser, with Tom Heaton producing fine saves from substitutes Marco Stiepermann and Onel Hernandez as Daniel Farke’s struggling side suffered a 13th league defeat.
Jordan Ayew’s fine individual late goal saw Crystal Palace beat West Ham 2-1 at Selhurst Park.
Robert Snodgrass gave the Irons the lead against the run of play in the 57th minute.
Palace were level in the 68th minute through a volley from Cheikhou Kouyate.
Just when it looked like the match would end all square, Ayew danced through the West Ham defence before chipping the goalkeeper.
Sheffield United and Watford drew 1-1 at Bramall Lane, with the Hornets climbing off the bottom of the table.
Gerard Deulofeu had silenced the home faithful when he fired Watford ahead after 27 minutes.
However, Oliver Norwood equalised from the penalty spot in the 36th minute after a VAR review upheld the decision following a trip by Will Hughes on George Baldock.
John Egan had a late header cleared off the line as Watford held out for a valuable point.
In the early kick-off, Tottenham came from behind to beat Brighton 2-1.
After Spurs saw a goal ruled out by a close offside call following a VAR review, Adam Webster put the Seagulls in front when he headed in a free-kick in the 37th minute.
England captain Harry Kane equalised after 53 minutes, before Dele Alli completed the turnaround with 18 minutes left as he finished off a flowing team move.
Manchester United came from behind to beat Newcastle 4-1 at Old Trafford.
Matty Longstaff put Newcastle ahead on 17 minutes, but United were soon level through Anthony Martial when his low shot squirmed past keeper Martin Dubravka.
Mason Greenwood then fired in a fine effort from just outside the area and Marcus Rashford’s header made it 3-1 shortly before half-time.
Martial making the most of a stray backpass from Sean Longstaff to wrap things up on 51 minutes.