An own goal from Doncaster Rover's Andy Butler gave West Ham their third goal
West Ham gained a routine win over League One side Doncaster Rovers to set up an FA Cup fifth-round tie against either Manchester United or Liverpool.
The Hammers went ahead in the second minute when Andriy Yarmolenko released Ryan Fredericks and his pull-back was steered into the net by Pablo Fornals.
Yarmolenko made it 2-0 as he lifted a finish over Doncaster goalkeeper Ellery Balcombe after Said Benrahma's pass.
Andy Butler scored an own goal and Oladapo Afolayan added a fourth.
Substitute Afolayan had only been on the pitch for eight minutes and netted his first Hammers goal from close range when Fredericks' shot was parried by Balcombe.
The fourth-round match between Premier League leaders Manchester United and last season's title winners Liverpool will be played at 17:00 GMT on Sunday, 24 January and will be broadcast on BBC One with coverage beginning at 16:30.
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West Ham v Doncaster as it happened, plus analysis and reaction from Saturday's fourth-round ties
Lawro's FA Cup predictions v Radio 1 DJ Jordan North
Doncaster came into the game at London Stadium fourth in League One and with seven victories in their past eight matches.
However, West Ham, seventh in the Premier League, could have finished the match off inside the opening 10 minutes as after Fornals' early goal, Manuel Lanzini and Yarmolenko both shot wide when well placed.
But Yarmolenko's calm finish after he raced on to Benrahma's through ball later in the first half ended any hopes of an upset.
Tomas Soucek twice had efforts saved by Balcombe in the second half, but Butler inadvertently extended West Ham's lead when Mark Noble's right-wing corner bounced off him into the net.
The visitors almost scored in the second half but Matt Smith's strike hit the crossbar before Afolayan sealed the win as the Hammers reached the fifth round for the first time in five seasons.
'The FA Cup is vitally important' - what they said
West Ham assistant manager Alan Irvine, speaking to BBC Sport: "Very professional and strong. It's another clean sheet and another win. We're delighted that players who were given the opportunity to start have taken that - it's what you hope for.
"There's no way we would play a team we didn't think were strong enough. Full marks to them in the way they approached the game. They have strengthened their claim for places.
"We have a squad of players who if we keep fit are strong enough to make changes. The FA Cup is a fantastic competition and it's vitally important we try to do as well as we can."
Doncaster boss Darren Moore, speaking to BBC Sport: "The message was clear to my players coming up against that quality of opposition, if you make mistakes, you get punished.
"There were some good things we did but ultimately we got punished. It's been a good cup run and we take the rough with the smooth.
"The players can be pleased at what they have done to help the club out financially. Best of luck to West Ham for the rest of the competition.
"This was a big test and we had a mountain to climb after conceding so early. But the thing is to learn from it for the remainder of the season and for the players' individual careers."
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Line-ups
Match Stats
Live Text
Line-ups
West Ham
Formation 4-2-3-1
1Fabianski
24Fredericks4Balbuena23Diop31Johnson
16Noble28Soucek
18Fornals10Lanzini9Benrahma
7Yarmolenko
1FabianskiSubstituted forTrottat 83'minutes
24FredericksSubstituted forBaptisteat 83'minutes
4Balbuena
23Diop
31Johnson
16Noble
28SoucekSubstituted forAfolayanat 70'minutes
18Fornals
10Lanzini
9Benrahma
7Yarmolenko
Substitutes
3Cresswell
5Coufal
15Dawson
21Ogbonna
30Antonio
34Trott
40Afolayan
41Rice
75Baptiste
Doncaster
Formation 4-2-3-1
1Balcombe
5Wright4Anderson21Butler24John
2Halliday14Smith
11Taylor3James10Lokilo
9Okenabirhie
1Balcombe
5WrightSubstituted forAmosat 79'minutes
4Anderson
21Butler
24John
2Halliday
14SmithSubstituted forRichardsat 64'minutes
11TaylorSubstituted forWilliamsat 70'minutes
3James
10LokiloSubstituted forSimoes Inacioat 64'minutes
9Okenabirhie
Substitutes
13Jones
16Amos
17Richards
18Williams
22Simoes Inacio
30Blythe
31Ravenhill
Referee: Robert Jones
Match Stats
Home TeamWest HamAway TeamDoncaster
Possession
Home67%
Away33%
Shots
Home20
Away4
Shots on Target
Home12
Away2
Corners
Home4
Away3
Fouls
Home9
Away8
Live Text
Post update
Match ends, West Ham United 4, Doncaster Rovers 0.
90'+4'
Full Time
Second Half ends, West Ham United 4, Doncaster Rovers 0.
90'+3'
Post update
Offside, West Ham United. Oladapo Afolayan tries a through ball, but Andriy Yarmolenko is caught offside.
90'+3'
Post update
Attempt blocked. Saïd Benrahma (West Ham United) right footed shot from a difficult angle and long range on the left is blocked.
90'+2'
Post update
Saïd Benrahma (West Ham United) wins a free kick on the left wing.
90'+2'
Post update
Foul by Brad Halliday (Doncaster Rovers).
90'+1'
Post update
Offside, Doncaster Rovers. Danny Amos tries a through ball, but Fejiri Okenabirhie is caught offside.
90'
Post update
Attempt saved. Ben Johnson (West Ham United) right footed shot from outside the box is saved in the centre of the goal.
90'
Post update
Attempt blocked. Saïd Benrahma (West Ham United) right footed shot from outside the box is blocked. Assisted by Jamal Baptiste.
89'
Post update
Oladapo Afolayan (West Ham United) wins a free kick in the attacking half.
89'
Post update
Foul by Tom Anderson (Doncaster Rovers).
88'
Post update
Dangerous play by Mark Noble (West Ham United).
88'
Post update
Danny Amos (Doncaster Rovers) wins a free kick in the defensive half.
86'
Post update
Foul by Manuel Lanzini (West Ham United).
86'
Post update
Reece James (Doncaster Rovers) wins a free kick in the defensive half.
84'
Post update
Attempt saved. Manuel Lanzini (West Ham United) right footed shot from outside the box is saved in the top right corner. Assisted by Andriy Yarmolenko.
83'
Substitution
Substitution, West Ham United. Jamal Baptiste replaces Ryan Fredericks.
83'
Substitution
Substitution, West Ham United. Nathan Trott replaces Lukasz Fabianski.
82'
Post update
Corner, Doncaster Rovers. Conceded by Ben Johnson.
80'
Post update
Corner, Doncaster Rovers. Conceded by Ben Johnson.
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