Everton have been drawn with Manchester City in the Capital One Cup semi-finals while Jurgen Klopp's Liverpool will have to overcome Stoke City in the last four.
Roberto Martinez's men were kept away from their arch rivals after beating Middlesbrough 2-0 but have a tricky task ahead of them in cup favourites City.
Liverpool's reward for thrashing Southampton 6-1 on Wednesday, where they went 1-0 down in the first minute, is a two-legged clash with Mark Hughes' side.
Goals from Gerard Deulofeu and Romelu Lukaku sealed the win for the Toffees while City eased to a 4-1 win over Championship side Hull.
Wilfried Bony opened the scoring for Manuel Pellegrini's men before a late Kelechi Iheanacho and Kevin De Bruyne's double made sure of the win.
The other semi-final sees Klopp's men face Stoke but their route to the last four was made difficult when Sadio Mane had given Southampton an early lead at St Mary's.
However, a Divock Origi hat-trick and a Daniel Sturridge double helped Klopp's men book a spot in the semi-finals.
Stoke had beaten Championship outfit Sheffield Wednesday 2-0 on Tuesday night thanks to goals from Ibrahim Afellay and Phil Bardsley.
Everton host City at Goodison Park for the first of their two-legged clash, while Stoke are at the Britannia Stadium for the first leg against Liverpool.
The first legs will be played week beginning January with the return matches played the week commencing January 25.