Lincoln City will play Arsenal in the FA Cup quarter-finals as reward for their stunning fifth-round victory over Burnley.
The fifth-tier club became the first non-league team in 103 years to reach the last eight with the biggest shock of the competition so far on Saturday.
Holders Manchester United play Chelsea, and Millwall, who beat Premier League champions Leicester, play Tottenham.
Middlesbrough face Manchester City or Huddersfield, who drew 0-0 on Saturday.
Arsenal reached the last eight with a 2-0 win at Sutton.
The replay between Manchester City and Huddersfield is provisionally set for Tuesday, 28 February at Etihad Stadium.
The quarter-final matches will take place on the weekend of Saturday, 11 March.
Full FA Cup quarter-final draw:
- Chelsea v Manchester United
- Middlesbrough v Huddersfield/Manchester City
- Tottenham v Millwall
- Arsenal v Lincoln
There are 88 places between National League leaders Lincoln and Arsenal.
Lincoln boss Cowley said his side had achieved a "football miracle" after beating Burnley 1-0 at Turf Moor with an 89th-minute winner.
It is the first time in the club's 133-year history that they have reached the quarter-finals.
Their next match is away to North Ferriby United on Tuesday, while they are also still in the FA Trophy and play Boreham Wood for a semi-final place on Saturday.
Queens Park Rangers, who joined the Football League in 1920, were the last non-league team to make the FA Cup last eight, in 1914. They were beaten 2-1 by Liverpool in their quarter-final at Anfield.