City's domination of the first half was absolute and the only surprise was it took a penalty for them to lead at halftime, De Bruyne slotting home in the 37th minute.
However, second-half substitute Ceballos scored the victor for Arsenal in stoppage time with a clever finish at the near post after the visitors caught the Blades cold with a quick attack from the restart.
Arsenal, a 13-time champion, will play Manchester City, and 12-time victor Manchester United faces Chelsea.
Liverpool de retour au sommet en Angleterre
Les Reds avaient fait leur part du travail mercredi, avec brio et dans le huis clos d'Anfield, en écrasant Crystal Palace (4-0). Avec 23 points d'avance sur le Citizens après la 31ème journée, Liverpool ne peut plus être rejoint au classement.
Newcastle were made to pay for that terrible miss two minutes later when Sterling cut in from the left flank before curling one into the far corner from the edge of the box to seal the win.
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.
Chelsea midfielder Ross Barkley turned in a cross from Willian in the 63rd.
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Ceballos, on loan from Real Madrid, fired home a low angled shot in the first minute of added time soon after David McGoldrick's late equaliser appeared to have sent the tie at Bramall Lane into extra time. So unless the Magpies can turn things around in the second half, City will be heading to Wembley to face Arsenal.
Man United beat Norwich 2-1 on Saturday in the other quarterfinal.
Southampton moved up one place to 13th and is a comfortable 13 points clear of the relegation zone.
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