BBC Reports That, Arteta, taking charge of his first home game since succeeding sacked Unai Emery, looked on course for three important points after Pierre-Emerick Aubameyang's early header put the Gunners in front.
Chelsea, with manager Frank Lampard making a first-half tactical switch when he introduced Jorginho for the struggling Emerson, were gifted an equaliser seven minutes from time when goalkeeper Bernd Leno hopelessly misjudged Mason Mount's free-kick to leave the substitute with a simple finish.
Chelsea struck again with three minutes of normal time left, Tammy Abraham turning Arsenal substitute Shkodran Mustafi far too easily in the area to beat Leno and complete the smash-and-grab raid.
Arsenal, who lost defender Calum Chambers to injury in the first half, will start 2020 11 points behind fourth-placed Chelsea and without a Premier League home win since 6 October.
Arteta learning the hard way
Arteta understandably looked downcast as he and his players took sympathetic applause from their fans after they were left stunned by Chelsea's late surge.
Arsenal, for the first half-hour, dominated a desperately poor Chelsea and there was much to encourage everyone inside a vibrant Emirates Stadium as the new era kicked into life.
The Gunners, however, ran out of steam towards the end of the first half as Chelsea, helped by Lampard removing Emerson and sending on Jorginho, started to dominate and continued to do so after the break.
Arsenal were resilient but were hanging on and ultimately it was a calamitous individual error and familiar defensive fragility that was to prove their undoing.
Leno's rush of blood left Jorginho with the easiest of finishes, although Arsenal certainly had a case to complain about his continued presence on the pitch after escaping that second yellow card.
And then Mustafi, on for the injured Chambers, was badly at fault when he allowed Abraham far too much time to control, turn and score the winner.
Arteta will have seen some good signs but ultimately old faults let Arsenal down. There is going to be no quick fix.
Lampard finds a way as Chelsea win
Chelsea boss Lampard clearly felt he got his team selection wrong by ditching his three-man central defence and introducing Jorginho after 34 minutes - and deserves great credit for seeing it was not working and putting it right.
It did improve Chelsea but in reality they could not get any worse in a feisty London derby which saw nine players booked.
They took complete control of possession and territory after the break, with Lampard's subsequent substitutions also having an impact.
Teenager Tariq Lamptey was a lively presence down Chelsea's right flank on his Premier League debut after replacing Fikayo Tomori while Callum Hudson-Odoi did well when he came on for Matteo Kovacic.
Lampard looked like he was going to be frustrated by Chelsea's lack of end product once more but they were given that late lifeline by Leno's dreadful error as well as the generosity of referee Craig Pawson in allowing Jorginho to stay on.
Abraham completed the comeback for a dramatic win.
There is a rollercoaster nature to this Chelsea side, as proved by their results, a home defeat by Southampton sandwiched in between wins at Tottenham and Arsenal, but they got the job done to cement their place in the Premier League's top four.
Man of the match - Jorginho (Chelsea)
'It was very cruel' - reaction
Arsenal head coach Mikel Arteta: "It was very cruel the way we lost it, in the first half we saw a lot of positives and saw what we are trying to implement. But the way we conceded was disappointing.
"It was clear why it was disappointing, I don't need to say any more.
"Our reaction was right, we were doing the right things, it is hard to dominate all periods of the game against this team. We started to defend too deep and our energy levels are in a different place to Chelsea's.
"We need to sustain those periods for longer periods in the game and against top sides. Individual errors cost you games but I can't fault the effort, commitment and for putting in place what we practised."
Chelsea boss Frank Lampard: "We were so awful for 30 minutes; slow, lethargic, nervous. The opposite of against Tottenham. We gave Arsenal everything they wanted. We made the change early, felt it had to be done. Second half we dominated.
Were there words at half-time? "Possibly. From my point of view you can accept a miss-pass but you can't accept lethargy in a London derby. The players were told that and they delivered. The second half was nothing to do with tactics it was all to do with spirit and desire