Arsenal will host Manchester United in the fourth round of the FA Cup, with Manchester City at home to Burnley.
Newport's reward for beating Premier League Leicester is a daunting drip to Middlesbrough, while Oldham - victors over Fulham at Craven Cottage - will travel to League One rivals Doncaster.
Wolves will head to either Shrewsbury or Stoke after beating Liverpool, Chelsea will host Sheffield Wednesday or Luton, while Crystal Palace and Tottenham rounded off the draw in an all-top-flight affair.
Fourth-round draw
Swansea v Gillingham
Wimbledon v West Ham
Shrewsbury or Stoke v Wolves
Millwall v Everton
Brighton v West Brom
Bristol City v Bolton
Accrington v Derby or Southampton
Doncaster v Oldham
Chelsea v Sheffield Wednesday or Luton
Newcastle or Blackburn v Watford
Middlesbrough v Newport
Manchester City v Burnley
Barnet v Brentford
Portsmouth v QPR
Arsenal v Manchester United
Crystal Palace v Tottenham
