But it needed a controversial refereeing decision by Mark Clattenburg to deny Albion victory after Villa defender Alan Hutton clearly used his arm to block a goal-bound header from Liam Ridgewell.
But Clattenburg and his assistant failed to spot the incident and the visitors survived to earn their 16th draw of the campaign.
Alex McLeish's side deserved their share of the spoils on the balance of play and were again left to rue failing to be more clinical in front of goal
Gabriel Agbonlahor, Chris Herd and Charles N'Zogbia all failed to make the most of gilt edged chances and Albion's Ben Foster was the busier of the two keepers.
The return of experienced defender Richard Dunne after a two and a half month lay-off with a broken collarbone also brought a steadying presence to the Villa back four.
Villa looked full of attacking intent in the early stages and Charles N'Zogbia found Stephen Warnock in space and his shot was blocked by Billy Jones.
But Albion nearly caught out Villa during their first serious counter-attack.
Carlos Cuellar failed to make clean contact on his attempted clearance from Shane Long's cross-shot after a determined run by the Republic of Ireland striker. The loose ball broke to 11-goal leading scorer Peter Odemwingie whose close-range back heel was blocked.
The first clearcut chance fell to Villa midfielder Chris Herd after 26 minutes.
Dunne showed good control to the right of Ben Foster's goal before sending over a low cross which landed in Herd's path. He struck his shot firmly enough but it flew straight at Foster who was able to make the save.
Agbonlahor, without a goal in 20 league games, then used his pace to get clear of the Baggies back four. But his touch was heavy inside the area and Foster was able to block his eventual shot.
Foster then blocked another shot from Agbonlahor, whose pace was causing problems for Jones, with his feet.
Warnock became the first player to be yellow carded after 36 minutes for bringing down Long who needed treatment before being able to resume.
Hutton followed Warnock into referee Mark Clattenburg's notebook after pulling back Jerome Thomas.
Brunt looked to handle a ball into the box from Hutton but Villa's penalty appeals were waved aside.
Albion were incensed when denied what appeared to be a clearcut penalty four minutes into the second half.
Ridgewell climbed above the Villa defence to power in a header from Graham Dorrans' corner. Hutton, who had already been booked, appeared to scoop the ball over the bar with his arm. But Clattenburg turned aside Albion's appeals.
Albion were looking sharper and Gareth McAuley headed just wide from a Brunt free-kick.
But Foster again came to Albion's rescue when he blocked a fierce close range attempt from N'Zogbia after he was completely unmarked from Agbonlahor's accurate cross.
Tempers were becoming frayed and Clark and Heskey were booked in quick succession for challenge on McAuley.
Cuellar came to Villa's rescue when he headed Odemwingie's shot off the line.
Albion were now looking more dangerous and Jonas Olsson was only inches too high with a header from a Thomas cross.
Villa probed for a winner in the closing stages and a mix-up between Olsson and Foster saw the ball break to Agbonlahor.
His cross was turned back by Heskey to Herd whose shot was blocked by Olsson.
Given produced a superb save with seconds remaining to keep out an Odemwingie volley from Thomas' cross.