The Cherries were in dreamland in North London as Philip Billing and Marcos Senesi sent Gary O'Neil's men into a two-goal lead, but Thomas Partey and Ben White restored parity for the Gunners before a sensational Reiss Nelson effort with seconds remaining sealed another brilliant comeback win for the table-toppers.
There was barely time for both sets of fans to take their seats before the ball nestled into the back of the net, as Billing took a mere nine seconds to silence the Emirates crowd.
Straight from kickoff, Bournemouth worked the ball out to the right, and Dango Ouattara's cross from the right flew under the boot of Gabriel Magalhaes and fell for Billing to lash home.
William Saliba and Partey were caught unawares as Billing ghosted in, but the Dane did not quite break the record for the quickest-ever Premier League goal - that feat still belongs to Shane Long's 7.69 second strike versus Watford in 2019.
Arsenal's response to going behind was a typically relentless one, but Neto was on song to deny Martin Odegaard and Bukayo Saka in quick succession on the four-minute mark.
A chaotic opening showed no signs of slowing down, as Aaron Ramsdale had to produce a phenomenal save to deny Ouattara doubling Bournemouth's lead in the 19th minute, and the Gunners' afternoon went from bad to worse straight after - Leandro Trossard going off injured and being replaced by Emile Smith Rowe.
With Chris Mepham's arm up in the penalty area in the 33rd minute, Arsenal were up in arms and believed that they should have had a penalty when the ball hit the top of the Bournemouth's defender's outstretched limb, but neither Chris Kavanagh nor VAR official John Brooks were convinced.
As expected, Mikel Arteta's men came out all guns blazing at the start of the second half, but Bournemouth's admirable rearguard action was still winning out, and one member of the Cherries' backline would send the away end into further pandemonium in the 57th minute.
A corner swung in from the left found the head of Senesi, who gave Partey the slip and directed a low header into the back of the net in front of the Bournemouth faithful, leaving a shell-shocked Arsnal with an even steeper mountain to climb.
However, it took Arsenal just five minutes to reduce the deficit, as Neto punched a corner from Saka clear, but Smith Rowe headed the ball back into the danger area, and Partey lashed home at the back post to spark a nail-biting final half-hour.
Smith Rowe was bizarrely taken off for Nelson only a few minutes later - a change perhaps sparked by his perennial fitness problems - but it was an inspired change from Arteta, as Nelson made an instant impact from the bench to help draw Arsenal level.
The Englishman was picked out on the left-hand side of the box by Partey and sent a chipped ball to the back post, where White's volley into the ground crossed the line before Neto could palm it away.
Unsurprisingly, Arsenal continued to huff and puff for the all-important third goal, but VAR was not on their side, as two more potential handball offences against goalscorers Senesi and Billing were waved away within a couple of minutes of one another.
Bournemouth would seemingly survive a six-minute period of added time, but Arsenal's remarkable never-say-die attitude proved telling, as the ball fell to Nelson on the edge of the box following a corner, and the attacker rifled home a wonderful effort into the far corner to spark absolute bedlam inside the Emirates.
Arsenal, somehow, remain five points clear of Manchester City in first place ahead of Thursday's Europa League last-16 first leg against Sporting Lisbon on Thursday, while Bournemouth - for all of their valiant efforts - remain 19th ahead of hosting Liverpool next weekend.