Having opened the scoring midway through the first half and then added a second on the stroke of half-time, the Blades then made it 3-0 halfway through the second half to virtually kill the game.
However, in the 85th minute a long free-kick was knocked down to Tony Stokes, who lashed home from close range. Three minutes later, Hammers pulled another one back when Stokes beat two men and crossed for substitute David Cowley to fire in.
With their tails up, the visitors pushed forward in search of an equaliser, but sadly it was a case of too little, too late, and the final whistle ended their chances of a memorable comeback.
Said Kevin Keen afterwards: "It was a tough game against a very strong Sheffield United team and I think it surprised a few of our lads to come up against that kind of opposition.
"We kept going, though, and I was very pleased with the way the team responded to the challenge and kept going until the final whistle. Another five minutes and we might have got an equaliser but, if I am honest, Sheffield United were the better team and deserved the win.
"It was a good experience for the players, though. It showed them the kind of physical demands they will have to face in professional football and I was happy with the effort and determination they showed."
Team: Behcet, Young, White (Tomkins 80), Norval, Andrews, Yao (Cowley 46), Brady, Singh, Ephrain, Allen (Davidson 46), Stokes. Subs unused: Kemel, Cumberworth.
by Danny Francis