The Hammers headed into the tie at Upton Park with a 2-0 advantage that they gained at the Cardiff City Stadium last week.
It was the visitors that started the better of the two sides without drawing home goalkeeper Rob Green into any action.
Their failure to turn possession into goals was punished by the hosts in the 15th minute. Cardiff failed to clear a corner from Matty Taylor and captain Kevin Nolan reacted quickest to head into the net from inside the six-yard box.
The same player called Marshall into action again in the 35th minute with a curling effort that the Scottish keeper was able to turn away for a corner.
West Ham's appearance in the final was all but confirmed five minutes before the break courtesy of Ricardo Vaz Te. The Portuguese attacker evaded his marker inside the area before going on to fire into the net from a narrow angle.
The home side continued to dominate after the restart, although they rarely looked like adding a third to their tally during the opening exchanges of the half.
However, Nicky Maynard staked a claim for a starting berth at Wembley when he beat Marshall from inside the area following a through pass from fellow substitute Henri Lansbury with one minute remaining.
What will have worried manager Sam Allardyce though are injuries to midfield duo Jack Collison and Kevin Nolan, who suffered shoulder and knee complaints respectively.