Chelsea will take on FA Cup holders Manchester City for a place in the final as Manchester United take on Coventry City.
The draw for the last four raises the prospect of a repeat of last season's all-Manchester final.
Treble-chasing City eased through with a comfortable 2-0 victory over Newcastle on Saturday while Chelsea saw off Leicester 4-2.
Coventry were the first team to book a trip to Wembley after their dramatic 3-2 win away at Wolves on Saturday. They were then joined by holders Manchester City, who then made light work of Newcastle with a routine 2-0 win in which Bernardo Silva scored both goals.
Chelsea, as ever, made it hard for themselves against Leicester. Two goals to the good at half-time, despite Raheem Sterling’s missed penalty, a remarkable own goal by Axel Disasi and a stunning equaliser from Stephy Mavididi had the Championship side purring.
However, a Callum Doyle red card switched the momentum back in Chelsea’s favour and goals from Carney Chukwuemeka and Noni Madueke in injury time settled the tie.
Manchester United joined them in the hat by beating Liverpool in a seven-goal extra-time thriller. Amad Diallo scored deep in extra time after Marcus Rashford made amends for a bad miss to lift Manchester United to a breathless 4-3 victory.
United's victory at Old Trafford kept alive their only hope of silverware this season and spoiled Liverpool's dreams of hoisting four trophies in manager Jurgen Klopp's final season with the team.
The semi-finals will be played at Wembley on the weekend of April 20-21.
The FA Cup final will also be played at Wembley on May 25, six days after the last day of the Premier League season.
