Kidderminster, the lowest ranked side remaining in the competition, defeated Reading in the third round on Saturday while West Ham beat Leeds.
Boreham Wood, the other non-league team in the draw, will face Championship leaders Bournemouth away from home, while Chelsea will play League One side Plymouth at Stamford Bridge after they knocked out Chesterfield.
Cambridge United, who knocked out Newcastle at St James’ Park, were drawn at home to Luton Town. Nottingham Forest’s reward for knocking out Arsenal will be a home tie against holders Leicester.
Tottenham vs Brighton, Everton vs Brentford and Wolves vs Norwich were the three all-Premier League ties.
FA Cup fourth-round draw
Crystal Palace v Hartlepool United
Bournemouth v Boreham Wood
Huddersfield Town v Barnsley
Peterborough United v Queens Park Rangers
Cambridge United v Luton Town
Southampton v Coventry City
Chelsea v Plymouth Argyle
Everton v Brentford
Kidderminster Harriers v West Ham United
Manchester United/Aston Villa v Middlesbrough
Tottenham Hotspur v Brighton & Hove Albion
Liverpool v Cardiff City
Stoke City v Wigan Athletic
Nottingham Forest v Leicester City
Manchester City v Fulham
Wolverhampton Wanderers v Norwich City
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