Two early goals from corners were just reward for the Merseyside club which dominated throughout but could not score again.
Both players scored from early corners as the Reds ran riot against a Villa side lacking top scorers Darren Bent and Gabriel Agbonlahor up front.
The result means the Reds have lost just once in their last 14 matches and can boast the same record at Villa Park as they try and keep the pressure on the sides above them.
It was a dominant performance from the visiting side which should have scored far more than the two goals. Poor finishing again robbed Liverpool of a more comfortable victory with Luis Suarez hitting the woodwork twice and other players failing to hit the back of the net.
Villa failed to earn many clear-cut chances with Nathan Delfouneso heading over and a series of long-range shots failing to trouble Pepe Reina in the Liverpool goal.
In a slow start to the match Charlie Adam was lucky to escape a booking for a crude challenge on Delfouneso, but Stiliyan Petrov’s free kick was a routine save for Reina.
Stewart Downing was roundly booed by the home fans on his return to Villa Park despite being the club’s Player of the Season. But, after having one routine shot easily saved, it was his corner from the right which saw Liverpool take the lead.
Jonjo Shelvey’s flick was met by Suarez who tried to copy the midfielder only to miss the ball. However, after Brad Guzan made the saves, the ball fell to Bellamy to bundle home from close range and give his side an early advantage.
Bellamy was on inspired form and causing the Villa back line all sorts of problems. His run earned another corner and he delivered the cross from the left which saw Skrtel beat Richard Dunne and Alan Hutton to the ball before flicking home his side’s second goal after just 15 minutes.
Only Tottenham has scored more than one goal against Liverpool in the league this season but the home side responded with Charles N’Zogbia firing narrowly over from around 25 yards out before finding the side netting after a quick break and a pass from Delfouneso.
The visiting side looked dangerous every time it got the ball on the flanks but Villa continued to press and probably should have pulled a goal back when Delfouneso headed over from around six yards out.
At the other end, the quiet Suarez nut-megged Petrov and slipped in Shelvey but his shot on the slide was tipped wide by Guzan.
Liverpool started the second half like the first and should have had the game rapped up in the opening minutes. First, Bellamy scampered down the left and crossed to the back post where Daniel Agger – who had started the move by winning the ball off Dunne – headed over.
Moments later the Welshman dispossessed Hutton and played in Suarez who lost the ball to Dunne. However, the Uruguayan won it back, side-stepped Collins, then managed to hit the underside of the bar when he looked certain to score.
Villa was contributing to its own demise. Warnock was next to give the ball away just outside his own area and Guzan had to make an excellent save diving to his left to deny Johnson.
McLeish responded by bringing on Barry Bannan for Heskey but after a couple of decent shots on goal from range by N’Zogbia and Delph. it was the away side which continued to create excellent chances.
First Suarez hit the post from a delightful chip and then Adam was allowed to run in on goal, but with Shelvey waiting for the pass, he opted to shoot from the edge of the box and his shot deflected off Collins and went wide.
Shelvey then had a chance to shoot after being teed up by Suarez but he could only blaze over.
As in the first half, the game quietened down towards the end with Liverpool happy to frustrate Villa's attacks. Dalglish felt able to take off Suarez and brought on Andy Carroll as his side eased to a comfortable victory.