A double strike from Billy Mehmet appeared to have set Tony Carr's team on their way to a comfortable 2-0 victory but Villa struck twice in the dying moments to snatch a point.
Hammers had taken the lead after just 10 minutes, when Mehmet cut in from the left and fired his shot low into the far corner of the net, and the young striker doubled his tally and his team's lead on the hour.
17-year-old defender Tom Laws broke out from the back and surged into the Villa half before sliding a pass into the path of Mehmet, who again shot across the goalkeeper to find the net.
The Hammers had other chances to extend their lead. Mitchell Cole hit the post, while substitute Freddy Eastwood crashed an effort against the bar, but Mehmet's double appeared to be enough.
In the 87th minute, though, some slack defending allowed Villa to pull a goal back and, with just seconds remaining, the hosts were left stunned when their opponents grabbed an equaliser.
Said Tony Carr afterwards: "It really was a sickener to lose a two-goal lead in the final minutes, especially after we had virtually dominated the game and deserved all three points.
"We had other chances, hit the post, hit the crossbar, but in the end we were very tired and just ran out of steam to let them back in the game.
"We had a very young side out there today, with two lads moving up from the under-17s, and Villa are a good side - they won the FA Youth Cup last season, but after leading for so long, it seems more like a defeat than just a draw."
Team: Jackson, McClenahan, Tattam, Laws, Blewitt, Sofiane (Akinsete 46), Carrick, Lumsden, Mehmet (Eastwood 75), Pearson, Cole (Bunce 89). Subs unused: Behcet.
Meanwhile, goals from schoolboy Ollie Allen (no relation to Paul, Martin and Clive by the way!) and San Lee were not enough to prevent the under-17s from going down 3-2 at Southampton.
After conceding a soft goal in the eighth minute, when a Southampton forward was allowed a free header from a free-kick, Hammers fell 2-0 behind 10 minutes before the break to leave them facing an uphill battle in the second half.
Allen brought his side back into the game with a neat finish five minutes after the interval following good work on the right by Sos Yao, but the Hammers couldn't find an equaliser and Southampton added a third with just 10 minutes remaining.
The visitors rallied in the final five minutes and saw a couple of decent chances go begging before Lee grabbed a goal in the dying moments, but there wasn't time to search for a last-gasp equaliser and the Hammers were condemned to their first defeat since October 5.
Kevin Keen said later: "The first goal was very disappointing and the second one just before half-time gave us a mountain to climb.
"We had a very young side out today, with six schoolboys in the starting line-up, and Southampton were probably a little too strong for us.
"I couldn't fault the effort of the boys, though, and they responded well in the second half. It ends our good little run, but we will continue to work hard and look to bounce back against Bristol City next week."
Team: Morgan, Henry, Parrington, Ketchell (Williams 80), Craig, Wright, Singh (Allen 46), Shaw, Tucker, Collington (Yao 46), Lee. Subs unused: White, Reed.