Arsenal, who haven't won the League Cup since 1993, will welcome Palace after the South London side registered yet another chastening defeat against Arne Slot's Liverpool, who have now lost six of their last seven games in all competitions.
Slot fielded a weakened team, seemingly prioritising Liverpool's huge fixtures against Aston Villa, Real Madrid and Manchester City in the coming days, but it was still another embarrassing result for the Reds, coming hot on the heels of a 3-2 loss at Brentford on Saturday that further dented their weakening Premier League title defence.
Cardiff - the only non-Premier League side remaining in the competition - have been handed a home fixture against Chelsea.
Holders Newcastle, who comfortably beat Tottenham 2-0 on Wednesday night, will face Fulham at St James' Park.
Fabian Schar headed Newcastle's opener from Sandro Tonali's 24th-minute corner, before Nick Woltemade nodded in the second goal from Jacob Ramsey's 50th-minute cross.
The Magpies lifted their first major domestic trophy since 1955 when they defeated Liverpool in the League Cup final at Wembley last season.
Pep Guardiola's reward for City's 3-1 victory away at Swansea is a home tie against Brentford, who hammered Grimsby 5-0 on Tuesday evening.
The quarter-final matches are scheduled to take place the week commencing December 15th.
EFL Cup quarter-final draw in full:
Arsenal vs Crystal Palace
Cardiff City vs Chelsea
Manchester City vs Brentford
Newcastle vs Fulham