Callum Wilson equalized in the 70th minute for Bournemouth before setting up Jordon Ibe for the victor in the 74th minute, intensifying Arsenal's problems in what could be developing into another crisis under Arsene Wenger.
The win saw Bournemouth climb to thirteenth on the Premier League table with 24 points.
"It's a fantastic win because we need to pick up our home form", man-of-the-match Wilson told Sky Sports. Get the app to get the game.
"It's a massive lift".
Arsenal came close after eight minutes as wing-back Ainsley Maitland-Niles struck the bar with a curling shot.
It was a selection that displayed the alarming lack of quality available to Arsene Wenger - who was also missing Mesut Ozil through injury - meaning the Gunners' boss was forced to field an XI which from the outset looked as though it would struggle for goals - and indeed that was the case. At the other end, Bournemouth had a strong penalty appeal waved away after Alex Iwobi appeared to handle the ball in the area.
But with a much-needed three points there for the taking, Arsenal capitulated against their spirited hosts.
It was Ibe's first league goal for Bournemouth.