But after dominating the first half against a sluggish home side, Arsene Wenger's team were forced to defend doggedly in the closing stages after Carl Jenkinson had been dismissed for two bookable offences.
The match started at a breakneck speed and, after Alfred N'Diaye had headed Craig Gardner's cross over the bar, Theo Walcott twice went close to giving the Gunners an early lead.
Olivier Giroud fired a left-footed shot wide before Arsenal took the lead in the 35th minute when Cazorla swept a low drive past Simon Mignolet after Walcott had created the opening.
Arsenal's first-half dominance deserved a second goal and Walcott almost provided it, only to fire wide from a good position.
Sunderland improved after the break as Arsenal suffered two blows. Firstly Jack Wilshere had to limp out of the action with what appeared to be a hamstring injury before Jenkinson was sent off just after the hour mark.
The former Charlton Athletic defender, who was only in the side as Laurent Koscielny had picked up an injury in the warm-up, was booked in the opening minutes after hacking Jack Colback down and picked up a second yellow card for fouling Stephane Sessegnon.
The whole tone of the match changed and, although Walcott hit the woodwork for Wenger's team, Steven Fletcher and Titus Bramble both wasted excellent chances to grab an equaliser for the Black Cats.