Aston Villa are the most prolific team in the Barclays Premier League at scoring from set-pieces, but knowing that does not make it any easier to stop them. After being outplayed for long periods, Martin O’Neill’s team extended their impressive away record with two goals in three minutes from dead-ball situations and threatened to add more gloom to the storm clouds hanging over Anfield.

Peter Crouch, on as a substitute, saved face for Liverpool, equalising two minutes from time, but it was hardly a matter of celebration for Rafael Benítez’s side as they drew for the fourth successive time in the league. Amid the off-field turbulence, Liverpool trail Manchester United and Arsenal by 14 points. Even their grip on the final Champions League place is imperilled. Everton, their fierce Merseyside rivals, hold that final position, but Villa could move into fourth place by beating Blackburn Rovers at home on Saturday.

The Kop were united in their vocal support for Benítez, as they turned on Tom Hicks and George Gillett Jr, the American owners, who seem to be toying with the idea of selling up for a profit only a year after buying the club. Benítez claimed that it was primarily poor fortune that cost his team two points after Villa, who have lost only once away from home since last February, came from behind to lead until Crouch’s late intervention.

“Sometimes you need luck,” Benítez said. “When you are attacking, playing well, creating chances, you need to score the second goal to win. Conceding two goals from set-pieces, from a game where you have created all the chances, you could lose the game, so in that way we have to be happy with a draw.”

Liverpool dominated for an hour, but had only Yossi Benayoun’s goal to show for it. Dirk Kuyt, the Holland forward, shrugged off the cloak of mediocrity he has been wearing this season to cut a sharper figure and, when he tickled a pass behind Martin Laursen for Benayoun to run on to, Villa were in trouble.

Although Stuart Taylor, the Villa goalkeeper deputising for Scott Carson, who was ineligible to play against his parent club, managed to block the Israel midfield player’s initial effort, Benayoun was swiftest to his feet even if it was Laursen, Villa’s free-scoring defender, who got the last touch as the ball went over the line.

Kuyt, Liverpool’s leading goalscorer in the league last season, was on his game last night, driving a wonderful cross low across the face of goal after being picked out on the right wing by Javier Mascherano. Only the final touch was missing. But that was the tale of Liverpool’s night — possibly their season, according to Benítez — and Villa capitalised.

Liverpool had looked sound defensively, as well, with Sami Hyypia, keeping his place despite the availability of Martin Skrtel, the new £6.5 million signing from Zenit St Petersburg, reliable before Villa’s set-piece machine kicked in.

When Stiliyan Petrov floated in his free kick, Liverpool failed to block Laursen’s run and, as the Denmark defender headed back across goal, Marlon Harewood, the substitute, scored with an acrobatic overhead kick in front of the travelling supporters. It was only the striker’s second league goal since a £4 million summer move from West Ham United, but Liverpool’s vulnerability was tapped.

A few minutes later, Olof Mellberg, a target for Juventus as his contract enters its final six months, saw his shot from wide on the right deflect in off Fábio Aurélio after John Carew headed on Wilfred Bouma’s free kick and Villa were dreaming of a rare win at Anfield.

Gabriel Agbonlahor could have sealed the game when, supported by the indefatigable Nigel Reo-Coker, he ran almost the length of the field a minute later, but delayed the obvious pass and ultimately could not quite find the finish to match the approach.

It was from a free kick of their own that Liverpool equalised, Crouch hooking home his shot after Aurélio’s free kick bounced off the shins of Jamie Carragher, leaving O’Neill leaping out of his technical area in frustration.

Villa’s record at Anfield is poor — they have not won there since 2001 — but their manager’s is good. Leicester City won three and drew one at Anfield under his guidance in the 1990s and he so nearly instigated another shock last night.

Without the injured Gareth Barry, their England midfield player and captain, Villa will take heart from such a result. “We had a great chance to make it 3-1,” O’Neill said, “but I thought it was a great effort, without our captain, from our lads.”

Liverpool (4-4-2): J M Reina – Á Arbeloa (sub: M Skrtel, 70min), J Carragher, S Hyypia, F Aurélio – Y Benayoun (sub: P Crouch, 80), S Gerrard, J Mascherano, H Kewell (sub: R Babel, 74) – D Kuyt, F Torres. Substitutes not used: C Itandje, X Alonso. Booked: Arbeloa, Mascherano.

Aston Villa (4-4-2): S Taylor – O Mellberg, C Davies, M Laursen, W Bouma – C Gardner (sub: M Harewood, 66), S Petrov, N Reo-Coker, A Young – G Agbonlahor, J Carew (sub: Z Knight, 90). Substitutes not used: T Sorensen, G Cahill, I Osbourne. Booked: Laursen, Young.

Referee: M Clattenburg.