Ozil was a picture of composure as he ran through on goal, chipped the keeper and cut inside two defenders before slotting in from close range for a dramatic winner.
Earlier on, Arsenal’s hopes of a repeat of their 6-0 win in the reverse tie were quickly dispelled when Jonathan Cafu put Ludogorets in front against the run of play by steering in a left-footed volley from a Wanderson free-kick.
Cafu turned provider three minutes later as he jinked past Kieran Gibbs and squared a ball for Claudiu Keseru to turn in as the Bulgarian side shocked the Gunners with a second in a frantic opening.
Granit Xhaka guided in a 15-yard shot from an Ozil cross to pull one back for Arsene Wenger’s side before Olivier Giroud expertly headed in Aaron Ramsey’s clipped cross to equalise.
Arsenal keeper David Ospina twice saved from Wanderson before Ozil secured his side’s progress into the last 16.