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.
– No home comfort for Chelsea –
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.
– Spurs strike back –
Mourinho’s Tottenham fell behind again at home to Brighton as Adam Webster headed in midway through the first half.
Spurs were shorn of the suspended Son Heung-min after his appeal against a three-match ban for a kick out at Chelsea’s Antonio Rudiger was dismissed.
But two of their other star men stood up to be counted as Kane swept home at the second attempt after his first shot was saved by Mat Ryan.
Alli then delivered all three points with a delightful chipped finish from an acute angle.
“It’s hard after a defeat to have confidence and we started poorly, it affects the confidence,” said Mourinho.
“Brighton have monsters in the air and it affected the self-esteem of our team.
“In the second half the players put all the negative aside and were very strong in their performance.”
Sheffield United are behind Tottenham only on goal difference as they missed the chance to close to within a point of Chelsea in a 1-1 draw with bottom-of-the-table Watford.
Gerard Deulofeu gave the Hornets an early lead as they looked to build on a 2-0 win over Manchester United on Sunday.
However, Oliver Norwood’s penalty quickly brought the Blades level and only the brilliance of Ben Foster to deny John Fleck from point-blank range denied Chris Wilder’s men a fourth consecutive win.
Crystal Palace climbed up to eighth and within six points of the top four themselves as they came from behind to beat West Ham 2-1 and hand manager Roy Hodgson his first ever Premier League win on Boxing Day.
Robert Snodgrass put the Hammers in front early in the second half at Selhurst Park, but Palace roared back as Cheikhou Kouyate smashed home the equaliser against his old club.
Jordan Ayew then produced a sublime individual run and finish in the final minute to snatch victory for the Eagles.
Aston Villa won the battle of two of the bottom three as Conor Hourihane’s fine strike was enough to beat Norwich 1-0.