Manchester United will host West Ham in the FA Cup fifth round, while Southampton will travel to Wolves after ousting holders Arsenal.
David Moyes' side cruised past Doncaster Rovers 4-0 and will now travel to Old Trafford in the fifth round after Manchester United beat Liverpool 3-2 in Sunday's heavyweight clash.
Wolves were the first side through to the fifth round, beating non-League Chorley 1-0 thanks to a long-range Vitinha strike, and will host Southampton, who ended Arsenal's defence with a 1-0 win.
Manchester City booked a fifth-round meeting with Swansea - but needed a late rally to see off Cheltenham 3-1 - while Spurs set up a fifth-round tie with Everton after late goals saw off a spirited Wycombe on Monday.
The fifth-round ties, which were made shortly after the fourth-round ones, will pit Barnsley with Chelsea, and could see Everton face Tottenham if Spurs can see off Wycombe at Adams Park in Monday night's tie.
FA Cup fifth-round fixtures
Tue Feb 9: Burnley vs Bournemouth - Kick-off 5.30pm
Tue Feb 9: Manchester United vs West Ham - Kick-off 7.30pm
Wed Feb 10: Swansea vs Manchester City - Kick-off 5.30pm
Wed Feb 10: Sheffield United vs Bristol City - Kick-off 7.30pm
Wed Feb 10: Leicester vs Brighton - Kick-off 7.30pm
Wed Feb 10: Everton vs Tottenham - Kick-off 8.15pm
Thur Feb 11: Wolves vs Southampton - Kick-off 5.30pm
Thur Feb 11: Barnsley vs Chelsea - Kick-off 8pm
FA Cup 2020/21 - key dates and draw
The FA Cup schedule has been confirmed, with the final set to take place at Wembley on Saturday May 15.
There will be no replays this season to help ease fixture congestion.
The draw for the fifth round took place at the same time as that for the fourth round.
- Fifth round: Wednesday February 10
- Quarter-finals: Saturday March 20
- Semi-finals: Saturday April 17
- Final: Saturday May 15