Mikel Arteta’s Gunners fell to an early Dominic Calvert-Lewin opener before Eddie Nketiah equalised in a frenetic match, before a brace from Pierre-Emerick Aubameyang sealed the victory, sandwiched between Richarlison’s effort moments before the interval, as Arsenal moved up to ninth.
Story of the game
The visitors – who arrived in north London having lost their previous five visits and who hadn’t won in 23 trips – shocked the home support by taking an early lead.
With the game barely a minute old, Calvert-Lewin, the scorer of England’s goal against Venezuela to lift the U20 World Cup in 2017, notched his seventh strike since new boss Carlo Ancelotti took over before Christmas to make it 12 in total this term.
The former Stalybridge and Northampton loanee shocked the Emirates crowd with an overhead kick in the second minute after a flighted Gylfi Sigurdsson dead ball into the box, which David Luiz failed to clear.
There was a question about whether the boot of the 22-year-old Toffees attacker was high and dangerous but VAR ruled his effort valid.
Arsenal attempted to gain parity as Hector Bellerin went close with a shot over the bar, while Shkodran Mustafi – sporting a new bleach white crew cut - headed over when well placed.
In a busy opening, Alex Iwobi fired over when he could have done better.
While Gunners supporters were pleased with his profligacy they showed their class by applauding his name when the teams were read out prior to kick-off – and when he was substituted for Bernard on the hour mark.
Another player who received support from the Arsenal faithful was the unfortunate Sead Kolasinac, who was forced to leave the field of play in the opening quarter after sustaining what looked to be a serious shoulder injury after falling heavily in the 18thminute, as starlet Bukayo Saka raced onto the field of play to replace the Gunners defensive man mountain.
Nicolas Pepe went close with a curling left-foot shot but Everton failed to heed the warning as Nketiah made it 1-1 in the 27thminute following excellent work from the newly-introduced Saka.
Bukayo Saka prompts Arsenal's fightback
The precocious 18-year-old raced down the left flank after good link-up play by Granit Xhaka before the highly-rated Nketiah slotted home past Pickford from close range.
Six minutes later Aubameyang put Arteta’s side 2-1 ahead after calmly finishing past Jordan Pickford after Luiz played him through a porous Toffees backline.
The dramatic turnaround was the least the Gunners deserved after clawing their way back into the game through incisive attacking verve.
However, Everton and Calvert-Lewin still remained a threat – as those of a certain vintage nodded sagely when informed that former Gunner Kevin Campbell was the last English Everton player to reach 12 goals so quickly in a season.
Yet it was a Brazilian, Richarlison – who had been booked moments before for a late challenge on Dani Ceballos - who levelled for a persistent Everton side, well-organised by the wily Ancellotti, moments before the break.
Yerry Mina flicked the ball on in a crowded box before the former Watford striker prodded the ball into the net from close range past Leno with the merest of touches to ensure a 2-2 scoreline after a frenetic first 45 minutes.
Aubameyang clinches victory for Arsenal
The match continued in the same vein moments after the restart when captain Aubameyang made it 3-2.
Mesut Ozil fed Pepe down the right flank whose excellent left-footed cross saw Aubameyang head home past Pickford as the scoring continued.
After such hectic jousting it was understandable the game fell into a lull by its previously entertaining standards.
Yet the fayre was enlivened by a series of fascinating vignettes, not least from Ceballos as the Real Madrid loanee showed new-found tenacity during a hard-fought second half.
While Ceballos was always an attacking threat it was his defensive solidity and hard work which also impressed the home support – so much so they gave him a standing ovation when he was replaced late on by Lucas Torreira.
As the clock ticked down Leno proved his worth with a superb point-blank save from Calvert-Lewin, even if the Gunners defence once again showed a worrying propensity for sluggishness when danger approached.
But as referee Stuart Atwell blew the final whistle for a deserved victory, the Gunners' defensive solidity became a matter for another day, as the Arsenal revival under Arteta gathered momentum to make it 10 matches unbeaten this decade.