Manchester United will play Chelsea with both ties to be played at Wembley over the weekend of July 18/19.
Manchester City stayed on course to defend their FA Cup crown by beating quarter-final opponents Newcastle 2-0 at St James' Park.
It took the Blues just a solitary goal just after the hour mark to book a semifinal spot, as Ross Barkley struck to drown Leicester City and set his side up for a clash against the league's' big guns.
Spanish midfielder Dani Ceballos netted an injury-time victor in a 2-1 win at Sheffield United, which had two goals ruled offside by video replay.
The hosts paid the price for that miss as immediately thereafter, as Raheem Sterling made it 2-0 for City with a well placed strike away from Darlow after cutting inside on the right flank from second-half substitute Phil Foden's pass.
Harry Maguire struck an extra-time victor as United saw off 10-man Norwich in the first quarter-final on Saturday, while Chelsea beat Leicester 1-0 on Sunday thanks to Ross Barkley's second-half strike. Ceballos pounced with a low shot, just four minutes after David McGoldrick had equalised from close range.
At Bramall Lane, forward Nicolas Pepe's penalty put Arsenal ahead midway through the first half, after United midfielder John Lundstram had an early header ruled out for offside.
Mikel Arteta's men have been drawn to face either Manchester City or Newcastle United in the next round.
Arsenal progressed to the semi-finals of the FA Cup after Dani Ceballos netted a dramatic victor in stoppage time to seal a 2-1 victory over Sheffield United.