With fellow hopefuls Chelsea and Manchester United also securing victories, the Gunners stayed fourth – but this was in much more emphatic style as they eased to a 5-1 win over a hapless Cherries side.
Eddie Howe's men have now lost their last nine league games away from the Vitality Stadium and were second-best for much of the night as Ozil and Mkhitaryan ran riot.
The pair scored the first two goals before Lys Mousset pulled one back for Bournemouth – only for Laurent Koscielny, Pierre-Emerick Aubameyang and Alexandre Lacazette to seal a comfortable win with second-half strikes.
While Bournemouth's struggles on the road continue, Arsenal have made their home something of a fortress and have won their last eight at the Emirates.
Those recent records would continue as Arsenal capped an early start by taking the lead through Ozil.
The German was picked out by Sead Kolasinac and lofted a cute finish over Artur Boruc, who could only get a weak palm onto the ball as it looped over his head.
Bournemouth responded well and created a couple of decent chances to level, the best falling for Ryan Fraser, whose strike was saved well by Bernd Leno in the Arsenal goal.
But, with Arsenal looking dangerous going forward, the last thing the Cherries needed was to give their hosts a helping hand.
They did exactly that as Adam Smith's wayward cross-field pass was collected by Mkhitaryan, who exchanged a mesmerising one-two with Ozil before slotting home to double the advantage.
But Arsenal were charitable enough to return the favour soon after as Leno played a short goal-kick into Matteo Guendouzi.
The France Under-21 international was challenged by Dan Gosling, who rolled a pass across goal for Mousset to finish for what was the 1000th Premier League goal conceded by Arsenal.
The points were secured soon after the restart, Mkhitaryan again involved as he crossed for Koscielny – whose effort was too strong for Boruc and crept over the line.
The woodwork then came into play at both ends, Ozil sliding an effort against the post before Gosling's deflected strike bounced off the crossbar moments later.
A three-goal cushion was secured on the hour as Aubameyang collected Mkhitaryan's through ball before rounding Boruc and tucking away his 16th league goal of the campaign.
Alex Iwobi, on for Kolasinac, flicked an Ozil cross into the side-netting before fellow substitute Lacazette drew a decent save from Boruc.
There was nothing the Poland goalkeeper could do as Lacazette bent home a superb free-kick after Charlie Daniels had fouled Lucas Torreira – the striker sending his effort up and over the Bournemouth wall to extend the lead further still.
Koscielny took a knock towards the end of the contest but Arsenal prepared for Saturday's north London derby in some style.