Kevin Nolan headed the Hammers in front from close range after 15 minutes, before Ricardo Vaz Te’s emphatic strike as the game approached half-time gave Sam Allardyce’s side a 4-0 aggregate lead.
Second-half substitute Nicky Maynard completed the rout as the game approached stoppage time with a thunderous effort.
West Ham will now face the winner of the other semi-final, in which Blackpool lead Birmingham City 1-0 after the first leg, as they chase a return to the Premier League at the first time of asking.
Cardiff were pursuing a two-goal deficit but struggled to create chances early on, though Kenny Miller felt aggrieved when he had a legitimate penalty claim turned down by referee Mike Dean after being bundled over by Winston Reid.
And, five minutes later, the Welsh side’s challenge was made even more difficult as West Ham went in front through Nolan, who nodded in from virtually under the crossbar after Carlton Cole’s header from a Matt Taylor corner was blocked.
Nolan congratulates fellow goalscorer Vaz Te
O’Neil was denied again, this time by David Marshall, who kept out the midfielder’s curling strike with a superb diving save after good work from Vaz Te.
But there was nothing Marshall could do about West Ham’s second goal, when Vaz Te latched onto a Guy Demel pass and blasted into the opposite corner from inside the penalty area with five minutes of the first half left to play.
The hosts continued to dominate and Cole headed onto the roof of the net, with Peter Whittingham’s wayward free kick all Cardiff could muster in response before the end of what was a deflating 45 minutes of football for Malky Mackay’s side.
It was a case of more of the same after the break for West Ham, but Allardyce was forced into a change when Jack Collison left the pitch with an uncomfortable-looking shoulder injury and was replaced by Arsenal loanee Henri Lansbury.
The pace of the game slowed as a result of the change and Cardiff struggled to create any openings in the same way as they had in the first half, with Miller firing over perhaps out of frustration with less than 25 minutes remaining for the visitors’ first chance of the second period.
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Mackay responded by removing Stephen McPhail and Kenny Miller for Filip Kiss and Don Cowie with less than 15 minutes left on the clock.
Cowie felt that he should have been awarded a penalty when he was brought down by McCartney, but match official Dean again waved away appeals.
It took Cardiff 81 minutes to have their best chance on goal as Liam Lawrence tried his luck from 20 yards, but shot harmlessly wide as the Welsh side’s play-off charge fizzled out.
Maynard, a late substitute, finished off the tie by firing beyond Marshall into the top corner after a clever pass from Lansbury.