That will be the perfect tonic for bedridden Fulham boss Chris Coleman as the Hammers paid the price for some expensive misses.
Ten days ago Fulham keeper Edwin Van der Sar single-handedly broke Hammers hearts at Loftus Road and in this replay he was again in equally defiant form from start to finish.
After holding Kevin Horlock's awkward early drive, the Dutchman pounced on to David Connolly's skidding 20-yard shot before then brilliantly tipping over Marlon Harewood's rising screamer.
As West Ham piled on the pressure, Brian Deane's close-range effort was deflected over while at the other end Steven Bywayter was equal to both Moritz Volz's fierce shot and Steed Malbranque's difficult drive from the edge of the box.
Roared on by an angry Upton Park crowd the Eastenders easily had the greater appetite for a quarter-final spot and it would have been a huge injustice if the unmarked Boa Morte had headed home from all of one yard just before the break.
But having survived one of the misses of the season, the Hammers emerged for the second half in an equally determined mood and Harewood's early dangerous low cross only needed a touch.
Midway through the half, Bywater clawed out Sean Davis' point-blank header and then the England Under-21 midfielder fired over as the Cottagers gradually began to impose themselves.
With 20 minutes remaining, the Hammers keeper tipped over McBride's 20-yarder before denying substitute Hayles.
But by now the Premiership side had gained the upper hand and when Carlos Bocanegra's lofted pass found fellow American McBride on 75 minutes the Fulham striker sent an unstoppable 15-yarder past the exposed Bywater.
Just three minutes later, Hayles secured that trip to Old Trafford when he tapped home Malbranque's far-post cutback and, as the Hammers reeled from that deadly double blast, Boa Morte picked up another return pass from Malbranque to prod a third past Bywater right at the death.