It proved to be a frustrating afternoon for hosting Liverpool, who failed to make the most of their lengthy spells in possession.
Here, Sports Mole has dissected the previous 90 minutes of action on Merseyside.
On target: 8
On target: 1
Was the result fair?
In terms of possession Liverpool were the dominant force. However, football is all about taking your chances and Arsenal certainly did that. For that reason alone, the Gunners fully deserved the three points.
As mentioned above, the hosts had long spells in possession. They never really looked like breaching the Arsenal net though, which will be a cause of concern for manager Brendan Rodgers.
It was an extremely professional performance from the Gunners. They soaked up everything Liverpool had to offer, before going on to notch two goals on the counter-attack. It will also have pleased Arsene Wenger to see two of his new signings (Lukas Podolski and Santi Cazorla) find the net.
Sports Mole's man of the match
It's too difficult to split Abou Diaby and Mikel Arteta so we are going to cop out and give the award to both of them! The duo bossed the midfield at times and got forward really well. Arteta in particular also shone while defending in his own half.
It's been an awful week for Pepe Reina. Having made errors against Manchester City and Hearts, the goalkeeper committed a third mistake for Cazorla's goal. The attacker struck the ball hard, but Reina really should have done better.
Howard Webb had several penalty calls to deal with and he looked to have got every decision spot on. The Englishman showed why he is regarded as one of the best referees in world football.
Liverpool: It doesn't get much easier for the Reds. Next up is a home encounter against bitter rivals Manchester United.
Arsenal: Having finally got their season off and running, the Gunners will welcome Southampton to the Emirates Stadium after the international break.