The lowest ranked team left in the competition, Yeovil, were rewarded with a huge tie against Manchester United.
And after eliminating Leeds, Newport will take on Premier League giants Tottenham.
Chelsea will host Newcastle in the fourth round if they can win their replay against Norwich.
Nottingham Forest will travel to take on Hull after knocking out the holders Arsenal.
Premier League leaders Manchester City will travel to either Cardiff or Mansfield after their replay.
Fourth round ties will be played across the weekend of January 26-29, 2018.
Winning clubs will receive £90,000 in prize money.