But a combination of a below-par performance and some fine saves by Robert Green meant they had to settle for their first goalless draw of the league campaign.
It means the Carling Cup semi-finalists have taken only one point from the last nine.
Martin O'Neill's side barely woke from their slumbers during the opening 45 minutes against a side ravaged by injury problems.
They dominated the second period but only spasmodically threatened to find a way past England keeper Green.
In contrast, the Hammers were cock a hoop after gaining the point which moved them above Hull and Wolves.
West Ham were unable to field a single experienced striker because of injuries to Carlton Cole, Zavon Hines and Guillermo Franco, and 18-year-old Franck Nouble was left to shoulder the goalscoring responsibilities on his first Premier League start.
And Nouble came close to breaking the deadlock after six minutes.
He burst forward from the half-way line and shook off the challenges of Villa centre-backs James Collins and Richard Dunne to find himself with only Brad Friedel to beat.
But, having done all the hard work, he then unleashed a shot from 12 yards out which ended up in the Holte End.
Hammers midfielder Radoslav Kovac became the first player to be yellow carded after 17 minutes for a challenge on Emile Heskey 20 yards out.
There was a lack of inspiration about Villa's play in the opening quarter of the game but Green was tested for the first time after 26 minutes.
Heskey found Ashley Young in space on the left and he cut inside and saw his cross-shot heading for the top corner before it was fingertipped away at full stretch by Green
The England keeper then excelled himself in turning aside a fierce Agbonlahor shot on the turn from 15-yards out as Villa finally came to life.
Green also did well to cling onto a teasing cross from overlapping left-back Stephen Warnock as Heskey challenged inside the six-yard box.
Heskey sent a volley wide of Green's right-hand post which he only half connected with from a Young cross but Villa were still guilty of too many misplaced passes before the interval.
O'Neill would have demanded a vast improvement from his side and they started the second half on the offensive.
James Collins failed to make full contact on a Young corner with his glancing header, but the woodwork came to West Ham's rescue after 49 minutes.
Heskey teed up a shooting opportunity for Milner on the edge of the box and his drive beat the dive of Green but clipped the outside of a post.
Dunne failed by inches to get on the end of a Young free-kick as the pressure started to mount on the Hammers goal and Carlos Cuellar fizzed a first-time drive over the bar from Milner's fiercely driven cross.
Both sides made a substitution after 56 minutes with Heskey replaced by John Carew and Parker, who looked to have suffered a recurrence of his hamstring injury, making way for Alessandro Diamanti.
Kovac was fortunate not to receive a second yellow card for a challenge on Villa skipper Stiliyan Petrov and referee Mike Jones made it clear to Hammers captain Matthew Upson that the midfielder was in the last chance saloon.
The warning was heeded by Gianfranco Zola who replaced Kovac five minutes later with Junior Stanislas.
Carew had the ball in the net after 61 minutes but it was ruled out for offside. Then Agbonlahor was just too high from 12 yards out when he should have at least hit the target.
Former Hammers defender Collins was fortunate to slice a cross from Stanislas over his own crossbar.
Green then made a hash of a clearance under pressure from Carew but Agbonlahor opted not to shoot with the goal gaping and his cross was cut out.
Collison was yellow carded for a foul on Petrov as Villa pressed for the winner.
Then Petrov and Stanislas squared up to each other as tempers became frayed and both were yellow carded.