The on-loan Manchester United midfielder found the net after good work from youngster Jack Grealish as Tim Sherwood's men eased their relegation fears
Manchester United loanee Cleverley has looked rejuvenated under the stewardship of manager Tim Sherwood and made it three goals in as many games by tapping home Jack Grealish's excellent centre just after the half-hour mark.
It was no less than the hosts deserved for a fine first-half showing at Villa Park and Cleverley had already been denied by Adrian before his opener.
Perhaps understandably Villa appeared nervy in the second half, but the FA Cup finalists did enough to claim a potentially crucial three points.
Villa have now won three of their past four league games and are four points clear of the drop zone with just two matches remaining - meaning victory at Southampton will guarantee their survival.
West Ham's season continues to peter out and last weekend's win over Burnley was the only victory in six for Sam Allardyce's men, who drop to 10th.
The hosts, unchanged from last week's win over Everton, started confidently and West Ham goalkeeper Adrian made a smart parry to keep out Cleverley's well-struck volley from Fabian Delph's diagonal pass.
Another Delph delivery led to a chance for Christian Benteke, who failed to make clean contact with Jores Okore's knockdown from a tight angle.
The breakthrough finally came in the 31st minute.
Grealish showed ex-Villa man Stewart Downing a clean pair of heels to get to the left byline and his teasing ball across the face of goal was tapped in by Cleverley.
West Ham were visibly frustrated and Morgan Amalfitano was perhaps lucky to escape punishment for aiming a knee at Cleverley, albeit with little force.
The visitors then saw Cheikhou Kouyate go to ground during a corner, but their penalty claims were waved away as Kevin Nolan was adjudged to have fouled goalkeeper Shay Given.
West Ham had started with the same XI that beat Burnley, but Allardyce made two changes at the break with Amalfitano and Nolan withdrawn for Alex Song and Nene – the latter showing his intent with a powerful long-range effort that just cleared the crossbar.
Villa appeared slightly edgy at the start of the half, but Charles N'Zogbia showed neat footwork to get past left-back Aaron Cresswell only to chip his shot into the side-netting.
At the other end former Villa defender James Collins saw a looping header tipped over by Given, while Enner Valencia had the ball in the net when he headed in Nene's cross - but the forward was flagged offside and replays suggested he was just in front of full-back Kieran Richardson.
West Ham pushed for an equaliser as the clock wound down, but it was Villa who nearly scored a second when substitute Gabriel Agbonlahor - returning from a hamstring injury - raced clear only to lose balance and shoot wide.