The Hammers headed into the game in fine form but were pegged back by the home side, who turned in a disciplined defensive display to earn a creditable draw at Villa Park
The pressure on manager Paul Lambert had been ratcheted up by the dramatic loss to Spurs, in which Villa conceded twice in the final six minutes following striker Christian Benteke's dismissal.
However, Villa produced a more disciplined defensive performance this time around to claim a first point since their 1-0 win at Liverpool on September 13, against a high-flying West Ham side buoyed by Diafra Sakho's recovery from a shoulder injury and Andy Carroll's long-awaited return as a late substitute.
Sam Allardyce's hosts always looked the most likely to score, but were frustrated by an impressive display from Villa goalkeeper Brad Guzan.
Guzan pulled off a string of saves, including a late one-handed stop to deny Carroll after the striker had headed goalwards following his stoppage-time introduction.
The draw - a repeat of last season's result in the corresponding fixture - sees West Ham extend their unbeaten league run to five games and move up to fourth in the top flight, while Villa remain dangerously close to the bottom three.
Gabriel Agbonlahor - restored to Villa's starting XI in place of the suspended Benteke - crafted the game's first real opportunity against the run of play in the 13th minute when he fired over the crossbar at the end of a surging run into the West Ham box.
West Ham responded well to that scare and tested Guzan on numerous occasions, defender James Collins seeing his near-post header saved before Mark Noble stung the American's palms with a fierce drive.
However, the best opportunity of the opening period fell to midfielder Stewart Downing, who went close to celebrating his return to the England set-up with a goal, only for his powerful shot from the edge of the area to be kept out following a well-worked move from the hosts.
Villa grew into the game as the contest meandered towards the interval and Andreas Weimann saw an effort punched away by Adrian.
Yet the visitors' defensive frailties were exposed in first-half injury time when Downing wastefully lashed high and wide at the far post following clever build-up play from Alex Song.
Midfielder Tom Cleverley curled narrowly over the crossbar as Villa emerged from the break with renewed confidence.
Lambert's men showed improvement in the second period but, for all their endeavour, the visitors found themselves hanging on in the closing stages.
Villa would have fallen behind had Sakho not displayed surprising profligacy from substitute Carlton Cole's cross, placing a free header wide.
Nathan Baker was taken off on a stretcher following an attempted tackle on Cole, yet Villa were able to hold on as Carl Jenkinson directed a late header straight at Guzan prior to the goalkeeper springing to his right to deny Carroll a dream return.