Lewis Cook of Bournemouth holds off Pierre-Emerick Aubameyang and Alexandre Lacazette of Arsenal during the Premier League match between AFC Bournemouth and Arsenal FC at Vitality Stadium.
Mikel Arteta got off to an underwhelming start as Arsenal manager with a 1-1 draw at Bournemouth as Chelsea slumped to another shock home reverse, losing 2-0 to Southampton, on Boxing Day.
Carlo Ancelotti had a more positive impact on his Everton bow as Dominic Calvert-Lewin's brilliant diving header earned a 1-0 win over Burnley.
Chelsea's defeat allowed Tottenham to move back to within three points of the top four as they came from behind to beat Brighton 2-1 thanks to goals from Harry Kane and Dele Alli.
The top two clash later when Leicester host Liverpool hoping to close the gap on the runaway league leaders to seven points.
Arteta got an early lesson in the flaws that have blighted Arsenal's season as they were caught out trying to play from the back to concede the opening goal when Dan Gosling put Bournemouth in front.
Pierre-Emerick Aubameyang again rode to the Gunners' rescue to equalise just after the hour mark and Arteta will be frustrated not to have won all three points as Alexandre Lacazette was denied a winner by a last-ditch challenge from Steve Cook.
After the highs of victory at Spurs as Frank Lampard got one over on his former manager Jose Mourinho, Chelsea again struggled when faced with breaking down stubborn defensive opponents in Southampton.
The Blues have now lost to West Ham, Bournemouth and the Saints in their last four home league games.
Southampton boss Ralph Hasenhuttl rested in-form talisman Danny Ings, but that decision paid off as his replacement Michael Obafemi scored just his second Premier League goal with a calm finish into the top corner on the counter-attack.
The visitors struck again to seal all three points 17 minutes from time when Nathan Redmond prodded past the onrushing Kepa Arrizabalaga at the end of a fine team move.
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