The Reds were 2-0 up through goals from Philippe Coutinho and Mohamed Salah before three quickfire strikes in the second half from Alexis Sanchez, Granit Xhaka and Mesut Ozil put the home side ahead only for Roberto Firmino to earn the visitors a draw.
After throwing away another lead, Liverpool stay fourth - a point and a place above Arsenal - but the terrible defending from both sides indicated they will struggle for Champions League qualification without improvement at the back.
Arsenal will be without Aaron Ramsey as the midfielder is still nursing a hamstring injury while Olivier Giroud is also set to miss out after limping off with a hamstring problem against West Ham.
Salah cleared up his relationship with his African team-mate Sadio Mane, saying that the Senegalese is his closest friend in the team.
James Milner sent Salah surging away down the right flank and when the Egyptian's cross deflected off Laurent Koscielny, it fell perfectly for Coutinho, who finished his lung-bursting run with a deft header over Petr Cech for his 11th club goal this season.
Firmino, though, spared his side's blushes with an equaliser.
Arsenal left the field to boos from the Emirates crowd after a mistake-ridden first half saw the hosts fail to muster a single shot on target, with Liverpool eyeing a repeat of August's 4-0 rout.
"We play such good football going forward and maybe sometimes we need to switch that off for five or 10 minutes".
It was the spark that Arsenal needed and they were level three minutes later thanks to a Simon Mignolet howler.
Suddenly, Liverpool were in disarray and Wenger's men struck again with a majestic move in the 58th minute.
The drama wasn't over and Liverpool recovered their composure to equalise in the 71st minute.