Titleholder Chelsea will host Manchester United in the FA Cup fifth round in a repeat of last season's final.
United will head back to London after beating Arsenal in the fourth round on Friday in another tough draw.
Manchester City, the other big team remaining in the draw, was handed a trip to either second-tier Middesbrough or fourth-tier Newport County, who will meet in a replay.
AFC Wimbledon and Millwall, the two so-called "giant killers" in the fourth round after beating Premier League teams West Ham and Everton respectively, were drawn against each other.
The draw was made on Monday. Games take place from Feb. 15-18.
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Bristol City vs. Shrewsbury Town or Wolverhampton Wanderers
AFC Wimbledon vs. Millwall
Doncaster Rovers vs. Crystal Palace
Middlesbrough or Newport County vs. Manchester City
Chelsea vs. Manchester United
Swansea vs. Barnet or Brentford
Portsmouth or Queens Park Rangers vs. Watford
Brighton or West Bromwich Albion vs. Derby County