Arsenal - with Samir Nasri in the line-up as his proposed move to Manchester City goes on hold - held their own until impressive youngster Emmanuel Frimpong was sent off with 20 minutes left.
Liverpool boss Kenny Dalglish reacted by introducing Luis Suarez and Raul Meireles in what proved to be the decisive move, as the pair were involved in both goals.
They combined before youngster Ignasi Miquel, on for early injury victim Laurent Koscielny, saw a clearance deflect off Aaron Ramsey into his own net after 78 minutes and Suarez applied a simple finish from Meireles's pass in the dying seconds to wrap up Liverpool's first win of the season.
Wenger cut a frustrated figure as luck deserted an Arsenal side depleted by injuries and suspension, and one still recovering from the departure of captain Cesc Fabregas to Barcelona.
Arsenal applied plenty of effort but look desperately thin on rescources, something Wenger must address urgently, whereas Dalglish was able to bide his time before bringing on Suarez to make an emphatic impact.
Dalglish was ecstatic at the final whistle, whereas Wenger must now fear his defensive options will be reduced further by Koscielny's back problem ahead of Wednesday's Champions League qualifier against Udinese in Italy.
Nasri received a mixed reception when his name was announced - but swiftly won over his detractors with an energetic and influential performance in the opening period, with youngster Frimpong also impressive.
Arsenal also had to regroup after the early loss of Koscielny with a back spasm. Young Spanish defender Miquel came on and Liverpool almost took advantage of the defensive readjustment as Andy Carroll rose to meet Stewart Downing's cross and produce an athletic save from Wojciech Szczesny.
Szczesny had an easier task to save from Jordan Henderson's header before Arsenal grew in confidence and started to threaten in the latter stages of the half.
Nasri demonstrated the verve that has made him such a coveted asset with a surging run from inside his own half that ended with him shooting just wide from 20 yards and Frimpong also forced a fine stop from Liverpool keeper Pepe Reina with a low drive.
As a downpour soaked The Emirates Arsenal almost made the breakthrough after 68 minutes when Andrey Arshavin found Van Persie in the area but Reina stuck out a leg to make a vital save.
Wenger rubbed his hands through his rain-soaked hair in sheer frustration, and he was not feeling any better two minutes later when Frimpong marred what had been a performance of real promise with a wild challenge on Lucas that earned him a second yellow card and dismissal.
Dalglish used Liverpool's numerical advantage to make a double substitution, sending on Suarez and Meireles for Carroll and Dirk Kuyt. Wenger's response was to replace Arshavin with Henri Lansbury.
When the deadlock was broken, it came in cruel fashion for Arsenal with 12 minutes left. Miquel, with Suarez in close attendance, attempted to clear only to see his attempt strike Ramsey and loop over the stranded Szczesny.
The energy visibly drained out of Arsenal and Suarez's late second only increased the pain for Wenger and Arsenal's increasingly frustrated fans.
Source: BBC Sport
This story has been reproduced from today's media. It does not necessarily represent the position of Liverpool Football Club.
Author: BBC Sport
