Goals from Nicklas Bendtner and a stoppage-time penalty from Cesc Fabregas were enough to secure the points but the Gunners had to sweat for every one of them.
The opening exchanges were dominated by the Gunners and they should really have been several goals ahead but for a series of last-ditch interventions from Sunderland defenders and the woodwork.
Samir Nasri, Fabregas and Theo Walcott were all denied by some desperate but effective defending.
A deflected shot from Bendtner hit the top of the bar before bouncing away to safety. Walcott in particular was causing the visitors and, in particular, George McCartney some intense problems with his searing pace.
The Gunners' flying winger could not quite manage a finish when he was twice put through on the right flank to leave McCartney in his wake. McCartney was moved to mark Fabregas man for man and Anton Ferdinand was switched to left-back.
Sunderland absorbed the pressure well and were set up for the counter-attack, like so many teams that have enjoyed success against the Gunners of late.
With Kenwyne Jones as the spearhead and Fraizier Campbell and Darren Bent in support the potential was there for an upset.
Campbell failed to pull the trigger when free in the Arsenal box, allowing himself to be crowded out of a good opportunity.
The Gunners did eventually take the lead through Bendtner in the 27th minute after a jinking run on the right side of the area by Emmanuel Eboue. The Ivorian's shot cum-cross across the face of the goal was not cut out and Bendtner nipped in to fire into the net from close range.
Some sloppy play in midfield by Aaron Ramsey in the 38th minute allowed Kieran Richardson to seize possession. He then slipped in Jones with a delightful ball that left the Arsenal defence flat-footed but the Sunderland striker dragged his shot wide of the left post.
The Gunners began brightly after the interval with Thomas Vermaelen coming within millimetres of connecting with a ball across goal as the Belgian defender slid in on 50 minutes and then Walcott had a shot from the right well saved by Craig Gordon.
The Sunderland keeper also denied Vermaelen with a flying save from the centre-back's 20-yard free-kick.
Arsenal had a fright in the 65th minute when Bent seemed to get away from Mikael Silvestre. The visitors alleged that he was being held back in the area, but the referee said no and Manuel Almunia was able to pounce to secure the ball.
At the other end the Gunners were queuing up to score a much-needed second, but they were again denied by Sunderland bodies and a series of saves by Gordon.
The Gunners wrapped up the game and took all the points with a stoppage-time penalty.
Fabregas was upended by Campbell on the left side of the area and the linesman flagged for a penalty, eventually given by referee Steve Bennett.