The Division One side exploited the gaps in the home team's defence as attack seemed the best form of defence for both teams.
It did not take long for the deadlock to be broken as the visitors went in front through Brian Deane after just four minutes.
Wolves had only themselves to blame as they failed to clear a cross and Deane was given time to chest the ball down and volley home from just inside the area.
It was no more than West Ham deserved after a bright opening and they doubled their advantage midway through the half when a cleverly worked free-kick move allowed Marlon Harewood to acrobatically turn the ball in from six yards out.
The hosts were stung into action and wasted little time in getting back into the game as Ioan Ganea grabbed his first goal for the club just two minutes later.
Silas - making a rare appearance since joining the club in the summer - cut the ball back from the right wing and the Romanian was given acres of space to trap the ball and pick his spot past Stephen Bywater.
With Wolves enjoying plenty of possession down both flanks it appeared an equaliser was on the cards.
However it was Alan Pardew's men who grabbed the decisive fourth and final goal of the game as David Connolly beat the offside trap to run through and finish beautifully past the helpless Michael Oakes.
Dave Jones attempted to get back into the game with three substitutions soon after the break and it was replacement Leon Clarke who wasted their best chances to cut the deficit.
The young forward headed over from just six yards out and then shot wide with Bywater grounded after denying Ganea with his legs.
Colin Cameron struck a post in the final few minutes as Wolves laid siege to the West Ham goal but they could not create enough pressure to keep their cup dreams alive.
