A 2-1 reverse at Chelsea on Friday (AEST) officially ended City's reign as Premier League champion and Pep Guardiola's men looked out to make a statement from the off at St James' Park.
De Bruyne, who turned 29, coolly slotted home a 37th-minute penalty in what was scant reward for a dominant first-half showing.
Sterling then added a fine second 22 minutes from time as City booked a last-four date with Arsenal at Wembley.
Riyad Mahrez blazed one over and bent another effort wide of the right post from 20 yards as City threatened early.
Karl Darlow twice denied Sterling in a match that was fast becoming an attack-versus-defence training drill.
It took a silly push from Fabian Schar on Gabriel Jesus to break Newcastle down, though, with De Bruyne rolling the resulting penalty into the bottom-left corner.
Aymeric Laporte headed narrowly wide just before half-time and Mahrez flashed another chance just over shortly following the restart.
Newcastle should have been level when Allan Saint-Maximin laid one on a plate for substitute Dwight Gayle, who astonishingly skied over from six yards with the goal gaping.
City immediately made Newcastle pay. Sterling drove at its defence and cut inside before curling a cute finish into the bottom-right corner from 20 yards.