Despite taking the lead at the Vitality Stadium, we suffered defeat on the south coast to make it five games without a win.
Hector Bellerin seemed to have put the Gunners in control early in the second half, but the hosts hit back with two goals in five minutes.
All the drama came after the interval, the first half was light on clear-cut chances for both sides.
The closest we came in the opening 45 minutes was when Ainsley Maitland-Niles struck the crossbar on 15 minutes. The ball fell to him alone in the area, and after taking a couple of touches to work the shooting opportunity, he bent a right-footed effort which deflected off the bar and away.
Alex Iwobi saw an effort from 20 yards pushed away for a corner as the Gunners, without the attacking flair of either Alexis or Mesut Ozil, looked to take the game to the relegation-threatened hosts.
Bournemouth were well in the game themselves, and were presented with an excellent chance when Maitland-Niles inexplicably passed the ball straight to Jordon Ibe on halfway line. Fortunately for Arsenal though, the winger lost control when bursting into the box.
Danny Welbeck had an effort saved at close range by Asmir Begovic, and Lacazette was unable to control the follow up, but it was Bournemouth who ended the first half in the ascendancy.
Calum Chambers made a superb diving block to deny Dan Gosling inside the area. Bournemouth were hardly playing like a side with just one win from their previous 12 games.
But early in the second half the advancing Bellerin made the breakthrough. Iwobi released the right wing back with an early pass, and although Begovic got something on the shot, he couldn't stop it from squirming over the line.
Bournemouth heads didn't drop though, and they continued to press forward. They got their reward when Callum Wilson nipped in between defender and goalkeeper to get his toe on a right-wing cross.
It went from bad to worse just seconds after an Arsenal substitution. Aaron Ramsey came on as we moved to a back four, and the Welshman hadn't touched the ball before Bournemouth went ahead. Ibe smashed home down the middle of the goal from a Wilson knockdown.
We were unable to work Begovic after that, as we suffered another disappointing away day in the Premier League.
What it Means
We stay in sixth place in the Premier League, five points behind Tottenham above us, with 15 games remaining. Arsène Wenger's men are still without a win in 2018.
It's a rare midweek off for the Gunners - the first for two months - and we return to action with a home game against Crystal Palace in the Premier League, on Saturday at 3pm. That will be followed by the second leg of the Carabao Cup semi-final against Chelsea, also at Emirates Stadium, four days later.
With Alexis absent, and Mesut Ozil and Olivier Giroud still injured, a lot of the attacking onus fell onto England forward Danny Welbeck. Here are some of his best moments.
35 - Welbeck Linked up well with Lacazette, ran onto a through ball and stabbed a first time shot, which Asmir Begovic saved well, racing off his line.
44 - Welbeck was dispossessed on the edge of the area by Steve Cook, just when it looked like the chance was opening up for him at the end of the first half.
47 - Welbeck swapped passes with Iwobi outside the area, and fed the ball to Hector Bellerin out wide, but the move broke down.
67 - His tenacity and hard work started another attack, when he won the ball before finding Lacazette.
69 - Welbeck is flagged just offside after running onto a Wilshere pass.
79 - He sets up Aaron Ramsey just inside in the area after a couple of stepovers, but the Welshman couldn't get the ball under control
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