The hosts were far and away the better side on the night, with the Cherries taking the lead just 20 minutes into the game through Charlie Daniels.
Callum Wilson fired a second from the penalty spot after a Granit Xhaka foul before the excellent Ryan Fraser added a third on the 57th minute mark.
However an Alexis Sanchez header, and a Simon Francis red card, sparked the most unlikeliest of comeback 20 minutes from time, which came through Lucas Perez's stunning volley and Olivier Giroud's stoppage-time effort.
With that, an Arsenal side who had looked disinterested and uninspiring for most of the game came from 3-0 down to earn what could be a valuable point going into the second-half of the season.
Bournemouth leave Arsenal speechless
A patient start to the game resulted in a limited number of chances from either side early on. Joshua King tested Petr Cech from distance seven minutes in, however the strike flew straight into the arms of the goalkeeper.
Arsenal were left shell-shocked in the 18th minute, when Tottenham Hotspur Academy product Charlie Daniels gave the Cherries the lead after some horrific defending from Hector Bellerin.
The Spanish full-back ventured too far from his position, allowing Daniels to exploit the right wing with the amount of space he was given. A long pass from Junior Stanislas was enough to set-up an attack, and Daniels was clean through on goal. The winger capped off the move with a low drive past Cech, to give Bournemouth the lead.
From bad to worse
Things got bad to worse for Arsenal, when Xhaka pulled down Fraser in the penalty box moments after Daniels had given Bournemouth the lead. Wilson stepped up to the spot, and rolled the ball past a hopeless Cech with a simple finish, to make it 2-0 to Bournemouth in under 20 minutes.
Arsenal woes continued to burrow deeper, as Francis Coquelin was forced to come off after the Frenchman picked up a slight knock earlier in the match.
The Gunners looked completely alien to the side that dismantled Crystal Palace just two days previous, and the appearance of Alex Oxlade-Chamberlain was the spark that ignited the the attacking flow for the visitors.
The English winger almost assisted Alex Iwobi in the 42nd minute, when the former Southampton player burst down the by-line and played a pinpoint cross to Iwobi, but the Nigerian’s shot flew just wide of the near post.
Bournemouth continue to riot
Despite an encouraging start to the second half from Arsenal, the hosts remained the brighter team.
Bournemouth thought they had scored a third goal on the 56th minute mark, when Harry Arter’s strike fired into the back off the net, however Michael Oliver and the linesman disallowed the goal after Arter’s strike clearly struck the arm of Wilson.
The decision didn’t last long in the mind of Bournemouth fans though, as Fraser made it three to the hosts after Bellerin was yet again caught sleeping down the left wing.
Daniels played a long ball down the left flank towards the feet of Fraser and the winger easily beat Bellerin with some silky dribbling and then a calm finish through the legs of Cech, which seemed to put Arsenal’s chances of a comeback way beyond them with over 30 minutes to go.
Arsenal were forced into another change shortly after Fraser made it 3-0 to the hosts, as injured defender Laurent Koscielny was brought off for Gabriel.
Arsenal find their rhythm
Yet Sanchez breathed new life into Arsenal after the Chilean winger pulled a goal back on the 70th minute mark. Ramsey’s cross found the head of Giroud, who headed the ball across the face of goal, and Sanchez dived in at the last second to head the ball past Artur Boruc.
Lucas Perez added a second goal for the Gunners five minutes after Sanchez opened Arsenal’s account on the evening. Sanchez played the ball to Giroud, who brilliantly flicked the ball behind his marker to Perez, who from a tight angle spectacularly volleyed the ball past Boruc at the far post, to put Arsenal back into the game in style.
Dan Gosling should had put the game to bed, and ended Arsenal’s charge for a comeback, when the midfielder was played through in goal after sneaking past the offside trap, however despite having all the time in the world, the midfielder skied his strike over the bar.
In a huge blow to Bournemouth but a boost to Arsenal, the hosts were then reduced to 10 men when captain Simon Francis was shown a straight red card. The right-back went studs first on Ramsey, and the referee instantly gave Francis his marching orders.
Giroud to the rescue
The 90th minute ticked over, and the board showed six minutes of added on time. A minute later, Giroud equalised for Arsenal. Xhaka whipped in a smooth ball from the left wing, and a leaping Giroud made enough connection with the ball to beat Boruc at his near post, to complete the most unlikely of comebacks for the Gunners.
The result sees Arsenal miss out on a chance to claim third place, with the Gunners now at risk of falling to fifth place should Spurs claim a point against Chelsea on Wednesday evening.