A fine footballing goal won this tight game for an improving Arsenal team but Eddie Howe will know the truth. A manager consumed by fine details, Bournemouth's coach will know that it was a communal and unforgivable dereliction of duty that cost his team here.
You can never switch off in the Premier League, not for a second. It doesn't matter who you are playing. Here, after conceding an unnecessary free-kick forty yards from their own goal midway through the second half, Bournemouth momentarily allowed their minds to wander and within 30 seconds the ball was in their net.
It was a pretty goal from Arsenal. Alex Iwobi's pass inside the full-back to the galloping Sead Kolasinac was particularly lovely and the subsequent low cross to Pierre-Emerick Aubameyang at the far post was absolutely perfect.
MATCH FACTS, PLAYER RATINGS AND LEAGUE TABLE
: (4-4-2) Begovic 6; Francis 6, Cook 6, Ake 6, Daniels 6.5; Brooks 7 (Stanislas 72mins 6), Gosling 6.5 (Cook 72mins 6), Lerma 5, Fraser 5.5; Wilson 7, King 7 (Mousset 80mins 6). Not used: Boruc, Surman, Defoe, Mings.
: King 45
: (3-4-2-1) Leno 6.5; Mustafi 6, Sokratis 6, Holding 6; Bellerin 6, Torreira 7.5 (Guendouzi 78mins 6), Xhaka 7, Kolasinac 6.5; Mhitatyan 5.5, Iwobi 6 (Ramsey 80mins 6); Aubameyang 6. Not used: Cech, Elneny, Ozil, Maitland-Niles, Nketiah.
: Lerma OG 30, Aubameyang 66
: Craig Pawson 6
MAN OF MATCH
: Lucas Torreira
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It was a goal that deserved to win a football match.
But watch again and you will see Bournemouth players with their backs turned or their gaze averted when Arsenal restart play. Five Arsenal players were involved as they funnelled the ball across the field and back again and not one of them had a single glove laid on them by an opponent.
So that was what it took to separate these teams. Bournemouth – whose bright start to the season is now under threat after three defeats – will feel they deserved something and probably did. Some things did not go their way and they were pressing very hard for parity at the end.
Arsenal, meanwhile, have improved on the field and in between the ears under the guidance of new manager Unai Emery and the statistics support that.
The London club are now unbeaten in 17 games since the middle of August and have scored at least twice in every one of their Premier League games away from home. If that continues, they will challenge for a top four place that most would have presumed to be beyond them at the start of the campaign. Progress, indeed.
Here, they didn't actually start very well but their recovery was impressive and sustained. They are still flawed and probably need a couple of extra players at least. But Emery was brave enough to leave Mesut Ozil on the bench after a dismal performance in his last away game at Crystal Palace and he was rewarded with a team performance that spoke of some greater solidity this season.
There was a little luck for Arsenal early on and Howe was rightly upset that an eighth minute goal from David Brooks was ruled out for offside. The 21-year-old was dangerous in an opening spell that Bournemouth dominated and beat Bernd Leno from seven yards after playing a ball in to the area and running on to return. He looked offside when he scored but he wasn't. Arsenal's Shkodran Mustafi was playing him on as he lay on the floor and the goal should have stood.
These things are hard to take at the best of times, even more so when you face a side as good as Arsenal. Emery's team, for their part, rode that luck and improved as the game progressed. Having said that, their opening goal was freakish.
The Colombian Jefferson Lerma played against England in the World Cup and is a formidable athlete. Here, though, he contributed a stunning own goal on the half hour, stretching to intercept a cross from Kolasinac and only managing to volley it powerfully past his own goalkeeper from 14 yards.
It was a once-in-a-career moment and it looked for a while as though it would sink Bournemouth. With the Uruguayan midfielder Lucas Torreira increasingly influential for Arsenal, they started to dominate possession and find space between Bournemouth's back four and midfield.
Another goal at this stage may have ended things but Bournemouth are capable to hurting the very best teams on the counter and here they stuck back in first half injury time.
As an Arsenal attack broke down in their opponents' penalty area, Bournemouth saw the opportunity to break and did so through Ryan Fraser and then Callum Wilson. Then, when the ball was moved infield to Brooks, he shifted it right to Joshua King who arrived to deliver a superb first time finish with his left instep across Leno and in to the far top corner of the goal.
Emery will not have been impressed with his players' failure to track the Bournemouth runners and right-back Hector Bellerin was most culpable. The Spaniard was jogging. Still, though, it was a fine goal and one that Bournemouth deserved.
The second half was even tighter than the first. For long periods there was not much in it all. After Arsena's second goal, Howe's brave use of substitutes helped his team mount a late charge and with the right bounce of the ball they may have taken something.
Emery's decision to take Torreira off perhaps affected his team more than he expected and when Lerma smacked a shot against the post from distance with five minutes to go, the Arsenal manager's relief on the touchline was clear.