Kenny Dalglish's men controlled large portions of the match against a Gunners outfit which seemed down on confidence and luck with central defender Laurent Koscielny succumbing to injury in the 15th minute (replaced by debutant Ignasi Miquel) before young midfielder Emmanuel Frimpong was dismissed for a second bookable offence 20 minutes from time.
The opening goal was very fortuitous for the Reds when Raul Meireles played in Luis Suarez in the 78th minute and as the Uruguayan flicked it back for his fellow substitute, the ball hit the chest of an unsuspecting Aaron Ramsey and looped over Wojciech Szczesny's head.
The fact that Suarez was off-side would hurt the Gunners but nonetheless, the goal stood and sent Liverpool on their way.
In the final minute of regular time, Suarez added a second which was created by Lucas Leiva who worked it to the top of the area before releasing Meireles. The Portuguese midfielder was on-side to slot it into the path of Suarez who finished with ease from close range to essentially wrap up proceedings.
Arsenal were lucky not to concede twice in the first half when Szczesny made saves from Andy Carroll and Jordan Henderson's headers whilst Frimpong and Samir Nasri provided the best chances for the home side in the opening 45 minutes but were unable to pierce Pepe Reina and the Reds defence.
Martin Kelly had the best chance of the match prior to the goals when he struck the near post from an angle in the 54th minute whilst Szczesny came up with two more vital saves with around 15 minutes left to deny the Reds.
Frimpong's horrendous challenge on Lucas in the 70th minute caused him to be the second Gunners debutant in two weeks to see red following Gervinho's dismissal at Newcastle United and will force Wenger to take a very hard look at his side after another goalless performance.
Red card:Emmanuel Frimpong 70'