Luis Suarez struck early as the Merseysiders had the better of the first 45 minutes in the capital.
© AP Photos
In what was a frantic opening to the match, the visitors were gifted the lead on five minutes.
Arsenal nearly equalised instantly, but Pepe Reina kept out Theo Walcott's curling effort.
Liverpool were soon up the other end trying to extend their advantage, only for Daniel Sturridge to drag his shot wide following an incisive pass from Suarez.
The away side then saw a chance cleared off the line when Daniel Agger rose highest from a corner before Suarez fired wide from a narrow angle.
Arsenal came close to finding the net in the final five minutes of the half as Olivier Giroud planted his header straight at Reina.
Jordan Henderson was put through in goal late on, but he could only clip his effort onto the roof of the net with Wojciech Szczesny coming out to meet him.