Nikica Jelavic's late goal earned West Ham a place in the fourth round of the FA Cup as they beat a dogged Wolves side 1-0 at Upton Park.
The Premier League outfit were matched by their Championship opponents until the final 10 minutes of a tightly fought contest, but Jelavic's sweetly struck volley clinched a victory the Hammers barely deserved.
Having beaten Liverpool and Southampton in their last two home fixtures, West Ham were favourites to advance to the fourth round, but the fluency and dynamism of their recent performances was missing, despite manager Slaven Bilic citing the competition as a priority for his side before the game.
Wolves manager Kenny Jackett will be doubly disappointed after seeing his side's brave performance amount to nothing, and forward Bjorn Bergmann Sigurdarson was carried off on a stretcher having only just returned to action after a long lay-off with a back injury.
West Ham can breathe a sigh of relief after avoiding a replay as they attempt to overcome a congested fixture list and achieve a top-six finish in the Premier League.
Wolves were without striker Benik Afobe, who is thought to be the subject of a £10million bid from Bournemouth, so new signing Michal Zyro started in attack for the visitors.
Despite their excellent recent home form in the top flight, West Ham struggled to settle into the game and they failed to trouble Wolves until Mauro Zarate cut inside and fired a shot straight down the throat of Carl Ikeme after 15 minutes.
The chance seemed to revive West Ham, and a deflected shot from Pedro Obiang drew a fine save from Ikeme, before Aaron Cresswell had claims for a penalty waved away when his shot appeared to hit a Wolves arm on its way wide.
Wolves sat back and absorbed the pressure effectively, and other than a Carl Jenkinson shot that Ikeme stretched to tip over the crossbar, there was little to worry Jackett before the break.
Zyro, who was at the centre of much of Wolves' best play in the first half, created their maiden chance after the interval with a mazy run that earned a corner. Rajiv van La Parra's short corner allowed Kevin McDonald to shoot through a crowded penalty area but Darren Randolph made a simple save for West Ham.
Sigurdarson's injury came as a cruel blow - making his first start in more than two years after recovering from back surgery, he went down unchallenged and had to be stretchered off.
Adam Le Fondre replaced Sigurdarson and Wolves continued to press through Zyro, who teed up David Edwards for a shot that was denied by a last-gasp West Ham clearance.
Le Fondre made a positive contribution, holding the ball up well and feeding Zyro, who tested Randolph with a good shot, but West Ham were given a late boost with the introduction of Dimitri Payet and Andy Carroll.
It was Carroll who provided the pass for Jelavic to break the deadlock, and the Croatian made no mistake in converting his first chance of the game with a fizzing volley that flew into the net.