Much-maligned all season and in grave danger of missing out on Champions League qualification after a drubbing at Tottenham Hotspur, United returned to the capital to produce one of their most vibrant displays of a poor campaign.
Teenager Marcus Rashford broke the deadlock with a sensational curling shot after 54 minutes before Marouane Fellaini's close-range effort sent United's 5,000-strong travelling fans barmy.
James Tomkins's header set up a nerve-jangling finale as West Ham threw the kitchen sink at David de Gea's goal but Andy Carroll headed a glorious chance over and the Spanish keeper produced heroics to repel a late onslaught.
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"I saw the gap in the corner and shouted 'shoot' and he did, but it's more difficult than you think," United manager Louis van Gaal, who introduced England skipper Wayne Rooney as a late substitute after a knee injury, told reporters of Rashford's goal.
"I said I wanted a title and I am very happy but, it's not about me, it is very important for the club," added the Dutchman whose side will face Everton in a Wembley semi-final.
The atmosphere was electric as West Ham kicked off their 155th and final FA Cup tie at the 112-year-old Boleyn ground, which they will leave for the gleaming Olympic Stadium next season, but after an opening burst the Hammers fell flat.
West Ham talisman Dimitri Payet struggled to conjure any magic and a tired-looking London side were tormented by Rashford, Jesse Lingard and Anthony Martial as United's slick passing took its toll.
Manager Slaven Bilic made no excuses for his side's first home defeat since August in the quarter-final replay.
"They were better tonight in the majority of the game. We had energy and commitment but they were killing us with ball possession," Bilic said.
"Apart from the first 15 minutes and final 20 they were the better side."
United, whose 11th FA Cup victory came 12 years ago, weathered an early storm and began to pick through West Ham with ominous regularity.
West Ham keeper Darren Randolph saved from Fellaini and Lingard before halftime, but he was a mere spectator as Rashford broke the deadlock.
Played in by Martial, the 18-year-old Rashford left Tomkins for dead on the edge of the area before finding the top right-hand corner with a sumptuous shot for his sixth goal for United.
Fellaini was rewarded for an industrious display when he deflected in Martial's driven cross to double the lead.
When Tomkins headed in for West Ham, United came under a ferocious aerial assault but Carroll headed over and De Gea made a brilliant double save to deny Cheikhou Kouyate and Carroll.
(Editing by Ed Osmond)
