The Gunners took the lead on the half-hour mark as Alexis Sanchez raced onto Wes Brown's poor back-pass and chipped the keeper.
Sanchez sealed the points for the visitors in stoppage time as he capitalised on a mistake from Vito Mannone to slot home from close range.
Here, Sports Mole takes a closer look at the events that unfolded at the Stadium of Light.
On Target 3
On Target 5
Was the result fair?
The better team won today's match, although the Gunners were not at their absolute best. They had plenty of possession and were in control for large periods, but their inability to build on their lead until the last minute looked as if it may cost them. As for Sunderland, it was a much better performance than last weekend's debacle at Southampton, but two huge defensive mistakes cost them dearly. They struggled to create any real chances and Gus Poyet will surely be under pressure following their start to the season.
Sunderland actually made a decent start to the match and their players seemed desperate to respond after their 8-0 defeat last Saturday. Although their opponents were dominating, they were holding solid until Brown badly underhit a pass back to Mannone, allowing Sanchez to run through and coolly chip the keeper. In the second half they showed a lot of fight and put in a number of tough challenges, but again a huge lapse in concentration cost them dearly as Mannone failed to clear the ball allowing Sanchez to score again.
It wasn't a vintage display from Arsene Wenger's side, but his players did enough to claim three vital points. They kept possession well and worked some decent openings without ever really tearing into the Sunderland defence. Both of their goals came from huge defensive blunders and they made sure to take advantage. The Gunners will face bigger tests this season, but make no mistake that it was important for them to come away from the North-East with a win that could help to revitalise their fading title hopes.
Sports Mole's man of the match
Alexis Sanchez: There weren't many standout performances this afternoon, but Sanchez takes all the praise for scoring both goals. His first was a moment of class, as he showed great composure to chip the ball past the keeper and he was in the right place to slot home the second late on and make sure of the points.
The biggest mistake of the match was made by Brown, who played a woefully short pass looking for his keeper, that was cut out by Sanchez. The Chilean ran through to score and the Black Cats faced an uphill struggle from that moment. Mannone's horrible attempt at a clearance must also be mentioned and the keeper may well be dropped for such an error.
Kevin Friend had plenty to deal with this afternoon as six players found their way into his notebook. He also allowed a couple of dangerous tackles from Jack Rodwell and Mathieu Flamini to go unpunished, but overall he managed the occasion well.
Sunderland: The Black Cats return to league action with a trip to Crystal Palace on November 3.
Arsenal: Arsenal welcome Burnley to the Emirates in their Premier League match next Saturday.