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Owen returned for his first start in a fortnight following a hamstring strain and was partnered by youngster Neil Mellor, while Senegalese star El-Hadji Diouf slotted in at left midfield.
In-form Dublin proved a constant thorn in the side of the Liverpool defence with his physical presence and commitment and volleyed over just minutes into the game.
Only minutes later Reds defender Stefan Henchoz dramatically cleared off his line after Dublin neatly lifted the ball over advancing Reds keeper Chris Kirkland.
Gerard Houllier's men, desperate to end their disastrous recent run, did themselves no favours as they struggled to keep hold of possession.
However, in the 24th minute, Owen almost opened the scoring following some neat passing between midfielders Salif Diao and the impressive Danny Murphy - but his shot ended up in the side netting.
John Arne Riise's well-struck half volley was deflected wide and emerging star Mellor's long-range effort was well saved.
On 38 minutes the Liverpool pressure paid off as Owen blasted home the opener.
Racing to the byline Diouf laid it back and after a deflection that looked like a hand ball from Villa's central defender Olof Melberg, Owen pounced and hammered home into the bottom right hand corner.
Villa began the second half even better than they started the first and within four minutes they had equalised with a Dublin penalty.
Reds captain, Sami Hyypia brought down Gareth Barry in the box and the former England man calmly slotted home from the spot.
Liverpool had ample opportunities to snatch all three points, as a Murphy free kick was cleared off the line and Steven Gerrard's long-range effort sailed just over the bar.
But yet again the Reds failed to deliver the killer punch as their slump continues with little hope on an end in sight.