The Gunners headed into the Boxing Day clash at Emirates Stadium having lost five of their past seven Premier League matches, yet were worthy winners against Frank Lampard's hapless team to mark the one-year anniversary of Arteta's first game in charge in style.
Alexandre Lacazette's penalty put Arsenal ahead in a league game for the first time since a win over Manchester United on 2 November (AEDT), and a stunning Granit Xhaka free-kick doubled its tally.
Bukayo Saka then embarrassed Edouard Mendy early in the second half though, after Tammy Abraham's goal – awarded after a VAR (video assistant referee) check) – Arsenal ultimately had to rely on Bernd Leno's save from Jorginho's penalty to prevent a nervy finish.
That meant Chelsea was condemned to a third defeat in four league games.
Moving six points clear of the bottom three will buy Arteta a little breathing space after talk he was in danger of the sack after just a year in charge.
Arsenal has only been relegated from the top flight once in its history, in 1912-1913.
With matches against Brighton and Hove Albion and West Bromwich Albion coming next in its Christmas schedule, Arsenal has a chance to climb to a healthy league position heading into 2021.
Having won the FA Cup final against Chelsea in August, Arteta has now delivered two major blows to Blues boss Frank Lampard this year.
Chelsea would have gone second with a victory, but instead remains six points behind leader Liverpool after a third defeat in its past four league games.
Lacklustre in attack, short of drive in midfield and bereft of a cutting edge up front, Chelsea's £200 million ($356.3 million) pre-season overhaul is yet to pay off.
Lampard has only 48 hours to lift Chelsea's flagging spirits before it is back in action against Aston Villa on Tuesday, the Villains fresh off an impressive 3-0 win over Crystal Palace, which they secured with only 10 men.