However, the visitors struggled to carve out clear openings and saw their hopes further hit when Arthur Masuaku was sent off for a second caution 23 minutes from time.
It left boss, Manuel Pellegrini frustrated on his 66th birthday as his side were forced to settle for a point that sees them move to eighth in the table.
Villa had the better openings in a match of few opportunities but couldn't step it up in the attacking third when they had the man advantage. Dean Smith will rue a missed chance to pinch another home win but will be pleased to see his side edge out of the drop zone and up to 17th.
West Ham will now turn their attention to Saturday's home clash with Manchester United, while Villa travel to Arsenal on Sunday.
A dour game most memorable for needle between teammates. Both sides will feel this was a missed opportunity to pick up a victory. West Ham remain unbeaten since the opening weekend and survived a very late surge from the hosts, but will believe they should have done more in attack.
Villa fought hard and carved out a couple of good openings. Their ability to come up with a solution to what appears to be a lack of firepower may well be key to their hopes of survival.
Overall, it was a dull battle that had plenty of gusto but lacked quality. It is perhaps fitting that the main talking point for supporters heading for the exits was a first-half scuffle that saw Anwar El Ghazi appear to head butt teammate Tyrone Mings after the Villa defender had a pop at the winger for failing to track back.
MAN OF THE MATCH
Lukasz Fabianski (West Ham). The Hammers keeper made a couple of important saves in a contest where defences were definitely on top.
ASTON VILLA: Heaton 7, Guilbert 7, Engels 7, Mings 7, Taylor 7, Nakamba 7, Grealish 7, Jota 6, McGinn 7, El Ghazi 7, Wesley 6. Subs: Elmohamady 6, Luiz n/a, Davis n/a.