Nikica Jelavic's first goal for West Ham fired them into the FA Cup fourth round at the expense of Wolves.
The former Everton striker, whose last goal came against the same opposition for Hull prior to his switch to Upton Park, struck with five minutes remaining to secure a hard-fought 1-0 win for the hosts.
Championship side Wolves arrived in east London without their 10-goal striker Benik Afobe amid talk of a £10million switch to Bournemouth.
But they did bring with them a miserly defence which had not conceded a goal in their last three matches, and they looked set to earn a replay until Jelavic broke the deadlock.
West Ham survived an early scare when Rajiv van La Parra's cross fizzed across the goalmouth with no one able to apply the final touch, but they went on to dominate the first half without finding a way through.
They appealed for a penalty when Danny Batth blocked Aaron Cresswell's drive but referee Anthony Taylor was not convinced, before Pedro Obiang forced a sharp save from Carl Ikeme at his near post with a deflected shot.
Obiang's header was also kept out by the Wolves keeper and Michail Antonio miscued a close-range volley from Carl Jenkinson's cross.
The closest they came to scoring in the opening half was from the unlikely boot of right-back Jenkinson, who collected Mauro Zarate's square pass and let fly from 20 yards, with Ikeme tipping the ball over the crossbar.
Wolves showed more ambition at the start of the second half but their momentum was halted by a worrying mystery injury suffered by striker Bjorn Sigurdarson.
The Icelander, starting his first Wolves match in over two years, collapsed to his knees with no one around him and was given lengthy treatment before departing the field on a stretcher.
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New signing Michal Zyro did manage to force a save from Hammers keeper Darren Randolph, while at the other end Obiang and Alex Song fired wide.
Hammers boss Slaven Bilic sent on the cavalry of Dimitri Payet and Andy Carroll with 25 minutes remaining, and French midfielder Payet immediately hit a free-kick on to the roof of the net.
But it was Carroll who played a big part in the winner, holding the the ball up on the edge of the area before feeding Jelavic, who crashed in a superb first-time shot which flew across Ikeme and into the corner of the net.
