The Blues, beaten finalists last season, went ahead in fortunate circumstances as Ben Chilwell’s low cross was steered into his own net by Blades midfielder Oliver Norwood.
Christian Pulisic was twice denied by away goalkeeper Aaron Ramsdale and Callum Hudson-Odoi shot over as the hosts looked to finish off the game.
David McGoldrick wasted a glorious chance to equalise as he sent a close-range diving header wide following John Lundstram’s right-wing cross, before home goalkeeper Kepa Arrizabalaga saved from Oliver McBurnie.
With Sheffield United pushing for a goal to take it into extra time, Chelsea broke in injury time and Hakim Ziyech scored their second with a low strike to take them into the last four for the fourth time in five seasons.
The semi-finals will take place at Wembley over the weekend of 17-18 April and the draw will be shown live on BBC One – during half-time of Sunday’s quarter-final between Leicester City and Manchester United (kick-off 17:00 GMT).