The Blues could however, increase their lead at the top of the table to seven points in the West London derby against QPR on Sunday.
Aaron Ramsey got the visitors off to a great start scoring on 12 minutes.
The Gunners have now won eight consecutive league games and the victory was also their first over Burnley in the league since 1970.
Özil completed a total of 77 passes at an 88 percent accuracy including four key passes – more than any other player over the 90 minutes.
Burnley – Arsenal
Stadium: Turf Moor
Referee: Mike Dean
Kick-off: 17:30 GMT
Burnley: Heaton; Trippier, Duff, Shackell (c), Mee; Boyd, Arfield, Jones, Barnes; Vokes, Ings
Subs: Gilks, Keane, Ward, Ulvestad, Jutkiewicz, Taylor, Kightly
Manager: Sean Dyche
Arsenal: Ospina, Bellerin, Mertesacker, Koscielny, Monreal, Coquelin, Cazorla, Ramsey, Ozil, Alexis, Giroud
Subs: Szczesny, Gibbs, Chambers, Flamini, Rosicky, Walcott, Welbeck
Manager: Arsene Wenger
Goals: 12′ Ramsey