Kai Havertz's early goal proved enough for the Gunners to emerge victorious on Merseyside as Arsenal now move three points above Manchester City at the top of the table.
The win comes just days after Arsenal were dumped out of the Carabao Cup on the road at Fleetwood Town as the EFL League Two side snatched victory on penalties after Max Dowman's red card.
The lessons learnt from losing in Lancashire were channelled by Arteta and his players against Andoni Iraola's team.
"This was for everyone attached to the football club. 14 years without winning here is a long time. We said after the last few days, after the defeat against Fleetwood, that things happen for a reason and that's going to give us another spring and hunger and belief to go and do it. What the team's done here today is incredible.
"They're in a really good moment. It was really deserved, to come here and win in the manner we have done, I think the players deserve so much credit."
Up next for Arsenal is a UEFA Champions League trip to Slavia Prague on November 4th.