Eddie Howe’s men were unchanged, while Arsenal brought in Oxlade-Chamberlain for Joel Campbell in their solitary switch.
The early stages saw Mathieu Flamini only booked for a heavy challenge on Dan Gosling which could have been punished more severely, while Alexis Sanchez lashed a shot over from a tight angle after latching on to Aaron Ramsey’s bouncing pass.
It was the match’s first shot on target which produced a goal from Ozil on 23 minutes. A deep cross from Ramsey was headed down by Olivier Giroud and the Germany international impressively arrowed a right-footed shot into the roof of the net.
Within 88 seconds, the lead was doubled. A poor piece of defending saw Steve Cook give away possession and Ramsey took advantage to slip a pass to Oxlade-Chamberlain, who directed an excellent finish in off the far post.
Bournemouth almost got back into the game when Harry Arter beat two men and unleashed an impressive dipping strike that was kept out by an acrobatic Petr Cech save.
Arsenal’s Nacho Monreal was denied a penalty by referee Kevin Friend after going down under Matt Ritchie’s challenge as the Gunners went into the break with a strong lead.
Both sides exchanged decent chances early in the second half, with Adam Smith forcing his way past Laurent Koscielny before firing a shot against the side netting for the hosts.
A few moments later, Sanchez collected a pass from Ozil at the other end and had a shot beaten away by Artur Boruc, with Arsenal settling for a comfortable two-goal victory.