Ozil put Arsenal ahead with his fourth goal of the season. Photo: Getty
Eddie Howe's Bournemouth were actually the in-form side heading into this one, unbeaten in four having won three of those games to move clear of the bottom three.
Mathieu Flamini was booked for an early two-footed challenge on Dan Gosling before Alexis Sanchez fired over from a tight angle with neither side able to establish a foothold in the game in the opening stages.
Arsenal finally started to dominate and it paid off as Oliver Giroud cushioned Aaron Ramsey's long ball into the path of Ozil, who fired home past Artur Boruc.
And, after such a long wait for a goal, the Gunners were soon two ahead as Oxlade-Chamberlain was fed by Ramsey before finishing with a low drive off the post.
Petr Cech during Arsenal's win at Bournemouth. Photo: AFP
Bournemouth almost got straight back into the contest but Petr Cech was on hand to brilliantly tip Harry Arter's curling effort over his crossbar.
Matt Ritchie wasted a good chance as he spooned over when picked out of the edge of the Arsenal box, with Howe's men still reeling from the quick-fire sucker punch.
Cech was again on hand at the stroke of half-time as former Tottenham youngster Adam Smith was picked out in the area, beating Nacho Monreal to the ball only to see the Gunners stopper close him down.
It was Smith who hit the side-netting with Bournemouth's first chance of the second-half before Sanchez's shot was pushed behind by Boruc for an Arsenal corner, from which Giroud headed straight at the Poland international.
The game petered out later in the half but both goalkeepers were called into late action, Boruc smothering Ramsey's effort before Cech capped a good display as he saved well from Steve Cook and Harry Arter.
All eyes will now be on the midday showdown between the Gunners and Leicester next Sunday, with Arsenal knowing they need another victory to truly be back in the hunt.
- Telegraph