FA Cup holders Manchester City will face Chelsea in the semifinals at Wembley, while Manchester United's reward for their thrilling win against Liverpool is a meeting with second-tier Coventry.
Sunday's draw for the last four raised the prospect of a repeat of last season's all-Manchester FA Cup final, which City won 2-1.
Treble-chasing City eased through to the semifinals with a 2-0 victory over Newcastle on Saturday.
Chelsea needed two stoppage-time goals to beat Championship promotion chasers Leicester 4-2 at Stamford Bridge on Sunday.
United came from 2-1 and 3-2 down to beat Liverpool 4-3 at Old Trafford on Sunday thanks to Amad Diallo's last-gasp strike in extra time.
United will play Championship side Coventry, who stunned Wolves 3-2 at Molineux on Saturday with two goals in stoppage time.
Draw for the English FA Cup semifinals made on Sunday:
Coventry v Manchester United
Manchester City v Chelsea
Ties to be played at Wembley on the weekend of 20-21 April.