The 27-year-old has been in scintillating form for the Gunners and racked up yet another assist before converting after a classy exchange with Olivier Giroud as they took advantage of Leicester playing on Tuesday to move clear at the summit.
Bournemouth had started well but a first Arsenal goal for Gabriel, who headed home an Ozil corner just before the half-hour mark, set the hosts on their way to a 2-0 victory.
After suffering a sobering 4-0 defeat at the hands of Southampton on Boxing Day, it was their south-coast rivals who were hoping to add to Arsene Wenger's Christmas woes.
Spurred on by recent wins over Premier League heavyweights Chelsea and Manchester United, Bournemouth had Arsenal against the ropes in the early going.
However, Eddie Howe's side could not muster a clear chance and were soon made to pay with their first lapse in concentration at the back.
Gabriel has not scored a goal since his time playing for Vitoria in his native Brazil but he powered home a header from Ozil's corner having given his marker the slip.
And the central defender, in for Laurent Koscielny after the loss at St Mary's not 48 hours earlier, came close to an improbable brace as he glanced a header onto the post minutes later.
The ball came back off the woodwork and into the path of his defensive colleague Per Mertesacker, but the Germany international showed less composure and somehow turned the ball wide from a little over a yard out and with the goal gaping.
Arsenal were starting to turn the screw and Theo Walcott should have doubled their lead when played through but Artur Boruc was equal to his low drive.
The second half began in much the same fashion as the first, with Bournemouth on top and pressing but unable to test Petr Cech.
But again it was Wenger's championship chasers who struck, Ozil playing a neat one-two with Giroud before controlling the ball and slotting coolly home.
Walcott then arrowed an effort just wide on a frustrating afternoon for the England forward as the hosts looked to kill off the contest.
Another Ozil cross was turned wide by Giroud before Bournemouth substitute Eunan O'Kane wasted their best chance as he curled a shot over the bar after being given the freedom of the Arsenal box.
In truth Cech's goal never came under threat as the Czech Republic goalkeeper took his Premier League clean-sheet tally to a record 170.
The game opened up in the closing stages and Alex Oxlade-Chamberlain nearly added a third but his shot was deflected behind with Walcott kept out by Boruc in injury-time having been freed by Ozil.
Arsenal allowed Bournemouth to keep possession as the clock ticked down, with referee Roger East's full-time whistle confirming the Gunners go top for at least a day.
TWEET OF THE MATCH
BOOM! Top of the League
BOOM! Clean sheet record for @PetrCech
BOOM! Mesut Ozil's a genius
#afc." @piersmorgan on Arsenal's win
Petr Cech: 6
Kieran Gibbs: 6
Per Mertesacker: 5
Calum Chambers: 6
Hector Bellerin: 6
Aaron Ramsey: 6
Mesut Ozil: 8
Theo Walcott: 6
Alex Oxlade-Chamberlain: 6
Olivier Giroud: 5
Joel Campbell: 5
Nacho Monreal: 5
Alex Iwobi: 5
Artur Boruc: 7
Simon Francis: 6
Steve Cook: 6
Dan Gosling: 6
Andrew Surman: 6
Marc Pugh: 7
Harry Arter: 6
Charlie Daniels: 6
Adam Smith: 5
Joshua King: 6
Matt Ritchie: 6
Eunan O'Kane: 6
Glenn Murray: 6
Mesut Ozil: Arsenal's most influential player this season produced another masterclass, providing the corner that Gabriel nodded home for the opener before showing a exquisite touch when combining with Olivier Giroud to finish a dazzling second
The German playmaker continues to track back in defence too, showing a greater appetite to help his team-mates when they do not have the ball.
MOMENT OF THE MATCH
For comedy value, Per Mertesacker's miss from point-blank range was worth a slice of the admission price alone
An attempt by Gabriel struck the left post and the ball rebounded on to the head of an unwitting Mertesacker who managed to nod wide before falling flat on his back, clasping his hands to his head in embarrassment.
VIEW FROM THE BENCH
Arsene Wenger made his substitutes with the game won at 2-0, bringing on Joel Campbell to offer fresh legs in attack and replacing Kieran Gibbs with Nacho Monreal
Bournemouth pair Eunan O'Kane and Glenn Murray made little impact off the bench.
MOAN OF THE MATCH
A frustrating performance from Theo Walcott, whose wastefulness in front of goal made heavy weather of a fixture Arsenal could have had sown up by half-time
The 26-year-old finds the right positions and his pace remains as frightening as ever, but his finishing still needs work and he is guilty of fading in and out of games.
WHO'S UP NEXT
Arsenal v Newcastle (Barclays Premier League, Saturday January 2)
Leicester v Bournemouth (Barclays Premier League, Saturday January)
Source : PA