Arsene Wenger's men are now without a win in five games in all competitions, and five points adrift of fourth place in the Premier League, after Bournemouth extended their unbeaten run to four games to move further away from the bottom three.
The breakthrough arrived early in the second half through Hector Bellerin, although it was a killer through-ball from Alex Iwobi that opened the game up.
However, Bournemouth produced a dramatic turnaround; first equalising in the 70th minute through Callum Wilson, who beat Petr Cech to the ball and slammed it home after an inviting cross from Ryan Fraser.
The Gunners started the match without Alexis Sanchez, with Arsene Wenger revealing before kick-off that the Chilean's future would be sorted imminently.
He said: "We were 1-0 up and suddenly we lost two goals and we don't know where they came from".
"Overall we have to look at it in a very objective and harsh way, as we made mistakes we should not have made".
Alexis Sanchez appears to be nearing his exit
"I think if you're looking at the blue-chip of years gone by; the Henrys, the Bergkamps, players like that".
"Alexis Sanchez, meanwhile, did not make the trip with the squad with Wenger confirming: "[He's] half in half out, you never know this kind of situation during the transfer period.
"It will be decided in the next 48 hours, it was a bit different for him because he was on standby a little bit, that's why I decided not to do it".
Arsenal must now dust themselves down as they look to get back to winning ways in the Premier League when they take on Crystal Palace at The Emirates next weekend. Very disappointing today, they didn't do enough for me. We have just tried to be very stable.
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Federer feels too old to be favourite
I think it's going to be helpful again for me this year because the court plays exactly the same in Perth and here in Melbourne . Perennial favourite Roger Federer will begin his campaign on Tuesday, as will Australia's highest-ranked woman Ashleigh Barty.