First half goals from Brian Deane, Marlon Harewood and David Connolly put Alan Pardew's men firmly in the driving seat and, despite a strike in between from Wolves striker Ioan Ganea, the Premiership strugglers were put to the sword after a battling second half performance.
The Hammers boss had been forced to alter his plans after Tomas Repka fell ill on the eve of the game. With new signing Andy Melville cup-tied, Hayden Mullins dropped back into the centre of defence alongside Christian Dailly, while Harewood filled a deeper role on the right and Deane came in up front for his first start since December 9.
The absence of the Czech defender may have been cause for concern but, just four minutes in, it was a case of every cloud has a silver lining as the veteran striker grabbed the opening goal to set Hammers on their way.
After Harewood's trickery on the right had beaten Naylor, the resulting cross was headed out to the edge of the penalty area and hooked back in by Etherington before dropping to Deane, who calmly chested down and planted a half-volley into the corner of the net.
Wolves almost levelled five minutes later when Stephen Bywater rushed out of his area to clear and diverted the ball straight to Silas, but Ferdinand was on hand to clear his goalbound effort off the line and Hammers responded to that scare by once again pushing men forward to put their opponents on the back foot.
Michael Carrick almost added a second on 15 minutes when he received Horlock's pass in space just 12 yards out but shot straight at Oakes and saw the rebound cleared for a corner.
Just six minutes later, though, the visitors did indeed double their lead. After Deane had been fouled 20 yards out, Connolly's clever free-kick released Harley, who clipped the ball to the far post where Deane turned provider and nodded down for Harewood to send an acrobatic overhead-kick past Oakes from six yards out.
Sadly, Hammers' delight at securing a two-goal cushion didn't last very long. Two minutes, in fact. A slip from Harley on the left let in Silas, who cut the ball back for Ioan Ganea to control 12 yards out and bend a curling effort past Bywater and into the net.
That gave the hosts an obvious lift but, having thrown away 10 leads already this season, Pardew's men were in no mood to make it 11 and came battling back in search of a third goal.
With Harewood and Etherington causing endless problems for full-backs Naylor and Luzhny, Hammers looked dangerous every time they attacked from wide positions, and it came as no real surprise when the two-goal advantage was restored 12 minutes before the break.
Etherington's clipped pass beat Luzhny and Connolly broke the offside trap to gain possession and cut in from the left before firing a blistering effort past Oakes and in off the bar.
The goal meant that Hammers took a 3-1 lead into the break for the second week running following last week's trip to Sheffield United, and avoiding a repeat performance of that disappointing late comeback from the Blades will no doubt have been on the agenda when Pardew gave his half-time talk.
Wolves manager Dave Jones replaced Luzhny with Jody Craddock before the restart in an effort to curb the dangerous running of Etherington but it was in attack that the hosts perhaps needed an extra impetus and, when the midway point in the second half arrived without Bywater having had to make a single save, it was clear that Hammers had learned their lesson when it came to defending a lead.
In the 68th minute, Wolves finally managed to create a clear-cut goalscoring opportunity, when Ganea burst clear to collect Cameron's flick, but Bywater followed up his tremendous penalty save at Bramall Lane with a superb block to deny the striker and, when substitute Clarke screwed the loose ball wide, it looked as though it would definitely be West Ham's day.
The young goalkeeper wasn't seriously tested again after that and when Cameron hit a post and saw the rebound cleared with three minutes left, the 5,000 travelling Hammers fans realised that a place among the last 16 was secure.
The magnificent support once again proved that the claret and blue faithful are the best in the land and, such is the atmosphere that they generate on their travels, there will be minimal complaint if Hammers are handed another away trip when the fifth round draw is made on Monday.
However, attention now reverts back to the league campaign, with a vital home clash against Rotherham United to look forward to, when the Hammers boss will have the cup-tied trio of Andy Melville, Nigel Reo-Coker and Adam Nowland available, and a hopefully well-again Tomas Repka in attendance.
The Alan Pardew revolution is now well underway and, while a return to the Premiership is still the obvious priority, Hammers fans will now also be starting to dream of a day out in Cardiff...