Aston Villa 0-2 Liverpool
Craig Bellamy inspired Liverpool to their fifth away league win of the season by scoring one goal and creating another in the space of four minutes.
The former Manchester City man fired home from close range after Jonjo Shelvey's clever flick created the opening from Stewart Downing's corner.
Bellamy then swung in a 15th-minute corner for Martin Skrtel to head home.
Charles N'Zogbia's effort in the first half was the closest Aston Villa came as they slumped to their fifth defeat.
Villa's final-day win over Liverpool at the end of last season was their first in 13 attempts but with the Reds having only one defeat in their 10 previous games before this visit, it was always going to be tough for the hosts.
And Alex McLeish's side's task was made even harder as a sluggish start saw them two down after only 15 minutes.
Downing, making his first visit to Villa Park since his £20m move in the summer to Anfield, squandered an early chance to a chorus of sarcastic cheers from the home faithful.
However, the Villa fans were soon silenced when Downing whipped in a corner that Shelvey diverted goalwards.
Luis Suarez attempted a trick of his own that Guzan blocked but Villa's second-choice keeper could do nothing to deny Bellamy smashing home.
Four minutes later, Skrtel grabbed his second goal of the season to double the visitors' advantage with Bellamy turning provider with a pacey corner that the Slovakian defender rose above Alan Hutton to head in.
With Gabriel Agbonlahor suspended and Darren Bent a late withdrawal because of injury, McLeish was missing his two top scorers and it was obvious as they created little in a first half that Liverpool dominated.
N'Zogbia was the one bright spark for the home side as he fired over just before the half-hour mark before hitting another effort into the side-netting soon after.
Bellamy continued to prosper after the restart as he crossed for Daniel Agger but the defender headed wide despite being unmarked at the back post.
Suarez, who was cleared to play after the outcome of disciplinary hearing on Friday was delayed, had a relatively quiet first half but he almost made it three with a move of real class.
The former Ajax forward was played through on goal and he beat both Richard Dunne and James Collins before rattling his effort off the underside of the crossbar.
That was the 16th time Liverpool have hit the woodwork this season and Suarez added the 17th just before the hour.
The Uruguayan found himself on the edge of the area with limited options his deft chip beat Guzan but not the post.
Charlie Adam then had a chance when he waltzed into the area but, with Shelvey in the clear to his left, the Scottish midfielder opted for a shot and it was deflected wide.
It would not prove costly, however, as McLeish's side failed to create another real chance and Dalglish got his first win away at Villa as Liverpool manager on his seventh attempt.