Certainly they bossed the first 45 minutes and have only themselves to blame as during this period thy missed a controversial penalty and had to rely on an own goal from an Arsenal defender to give them the lead.
Dirk Kuyt it was who missed the spot kick after Luis Suarez was brought down by Gunners keeper Wojciech Szczesny, and whilst television replays remained inconclusive as to the penalties validity, Suarez certainly made the most of the contact.
The Dutchman saw his effort saved then Szczesny reacted well to save the follow up from Kuyt.
But three minutes later the Reds deservedly went ahead as Jordan Henderson’s low cross created panic in the visitor’s rearguard and Laurent Koscielny’s hacked clearance flew into his own net.
With the home side looking comfortable against a disappointing Arsenal the side from North London quickly restored parity.
The half also saw Suarez and Kuyt hit the woodwork and how Liverpool would rue those missed opportunities.
The second half never quite lived up to the open nature of the first, not helped by a long delay caused by a serious head injury to Mikel Arteta.
Alex Song dinked through a ball which became goal number 35 of the campaign as van Persie volleyed imperiously home in the 91st minute.
Liverpool failed to respond in the remaining seven minutes leaving them 10 points adrift of the Premier League's top four.
Referee: Mark Halsey
Yellow cards: Vermaelen (ARS)