Marcus Rashford and Marouane Fellaini fired Manchester United to Wembley as West Ham's last ever FA Cup tie at Upton Park ended in a 2-1 defeat.
The Hammers went into the quarter-final replay as favourites to see off a United side enduring another tough season amid rumours of dressing room disharmony and mounting criticism of boss Louis Van Gaal.
The youngster still had plenty to do, but he stepped inside James Tomkins before curling a superb shot beyond Randolph and into the top corner for a 54th-minute opener.
West Ham felt they should have been awarded a penalty moments later when Daley Blind blocked Dimitri Payet's run in the area but referee Roger East was unconvinced.
Instead they fell two behind when Lingard's cross was blasted back across goal by Martial and diverted into the net by the knee of Fellaini (67).
West Ham should have been down and out but they at least made a game of it when Andy Carroll nodded Payet's corner into the six-yard box and Tomkins bravely stooped to head past De Gea with 11 minutes left.
In a frantic finale Carroll headed narrowly over and De Gea made a superb save to deny Kouyate, before the midfielder's header was ruled out by a narrow offside decision.
Confirmed semi-final ties
Everton vs Manchester - Saturday April 23 - 5.15pm
Crystal Palace vs Watford - Saturday May 21 - 4pm
We look at five key talking points ahead of the contest at Upton Park, where the prize for the winner will be a last-four Wembley clash with Everton.
What is known for definite is that if United lose on Wednesday, it will be game over in terms of their hopes this season of claiming their first trophy since 2013. It will also, surely, leave things looking more bleak than ever for Louis van Gaal's reign as Red Devils boss. Following Sunday's 3-0 Barclays Premier League loss at Tottenham, which left fifth-placed United four points off fourth spot, there has been renewed questioning over the Dutchman's position, while reports have suggested his relationship with some of his players has become strained.
HOW WILL UNITED LINE UP?
There has been much bafflement - including, reportedly, from members of the playing staff - at some of Van Gaal's tactics, not least on Sunday during a match which saw him at one point deploy winger Ashley Young as a centre-forward. It would be fair to say it feels difficult to predict exactly how the team might look on Wednesday night.
ROONEY TO RETURN?
One particularly notable unknown is whether United skipper Wayne Rooney will be involved. The forward got his first run-out since sustaining a knee injury in February when he played 61 minutes for the club's Under-21s on Monday, and Van Gaal had previously indicated Rooney could make his first-team comeback in Wednesday's clash.
CARROLL ON SONG
West Ham have a frontman looking very much fit again in Andy Carroll, whose hat-trick against Arsenal on Saturday has prompted talk about his chances of joining Rooney in the England squad for Euro 2016, and certainly caught United's eye. Van Gaal has spoken about his wariness of Carroll's threat, while Hammers boss Slaven Bilic has labelled the player "very special".
CUP CONCLUSION FOR UPTON PARK
Bilic's description of Carroll would also seem apt for the entire occasion on Wednesday, when West Ham, whose home matches will be at the Olympic Stadium from next season, play a cup game at Upton Park for the last time. All connected to the London club will be keen for it to prove a triumphant finale, and it will be interesting to see how the atmosphere generated by the crowd appears to impact on proceedings.
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