Olivier Giroud scored the decisive goal midway through the first half at the Emirates Stadium to see the Gunners move up to fourth in the table.
Meanwhile, the result saw Spurs lose their 100% start to the campaign.
Here, Sports Mole takes a closer look at the action in the North London derby.
On target 5
On target 4
Was the result fair?
While both sides created chances in front of goal, Arsenal deservedly picked up the win thanks to a blend of dynamic attacking play and robust defending. This was not a classic North London derby, but the Gunners took more risks and looked as if they wanted it more.
This was the sort of display that gets manager Arsene Wenger beaming from ear to ear as his players battled against the odds to get the victory. Their play in the final third was typically slick, while the defence stood extremely firm to withstand moments of Tottenham pressure. Unfortunately for Arsenal fans, what it all means is that the club are now less likely to spend in the transfer window.
Spurs manager Andre Villas-Boas is sure to be disappointed with his side for their lack of creativity and ideas throughout the 90 minutes. Tottenham had plenty of talented players out on the pitch, but none of them stepped up to take the game by the scruff of the neck. It is likely that the club's raft of summer signings will need time to settle into life in the Premier League, but too many of them went missing at the Emirates Stadium.
Sports Mole's man of the match
Tomas Rosicky: The Czech midfielder was an energetic presence for Arsenal at both ends of the pitch as he linked play well in attack while chasing the ball down in defence when necessary. If he stays fit, then the 32-year-old could have a major say in where the Gunners finish this season.
Nacer Chadli had a frustrating afternoon for the visitors out on the left wing, and he added to that frustration late on by shooting well over the crossbar when he had a number of teammates waiting in the middle for a cross.
In what can so often be a feisty fixture, Michael Oliver remained calm throughout and got all of the key decisions right without hampering the flow of the match too much.
Arsenal: The Gunners are back in Premier League action in two weeks' time when they travel to Sunderland.
Tottenham: Spurs will look to get back to winning ways when they host Norwich City.