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.
Newcastle did improve marginally after the break and substitute Dwight Gayle somehow missed a gaping goal.
One minute later Sterling curled home a delightful effort to seal City’s progress and set up a semi-final against Arsenal.
All four of this year’s Cup quarter-finals, all played behind closed doors, were won by the away team — the first time that has happened since 1987.
Manchester United will face Chelsea in the other semi-final.
“We are in the semi-finals. It was not easy to attack against a team defending so deep but it was a good performance. I am happy to go back to London, to Wembley,” City manager Pep Guardiola told reporters.
After their midweek defeat at Chelsea, a result that confirmed Liverpool as Premier League champions, Guardiola’s side were fired-up at an empty St James’ Park.
Twenty five minutes into the tie, Newcastle had completed only 15 passes and were camped inside their own penalty area as City toyed with them.
Riyad Mahrez wasted three chances for City and Sterling was twice denied by Newcastle keeper Karl Darlow.
Having somehow survived the City onslaught, Newcastle then gifted City an opening goal when Fabian Schar needlessly shoved Gabriel Jesus and de Bruyne tucked away the penalty.
Newcastle showed more intensity after the interval with striker Andy Carroll throwing his weight around but their absent fans watching at home on TV would have been groaning when Gayle somehow fired over the crossbar from Allan Saint-Maximin’s low cross.
That glaring miss looked even more costly a minute later when Sterling, who was inspired throughout, cut in from the left and picked out the bottom corner with a clinical finish.
City may have lost their English crown, but having already bagged the League Cup and still in the Champions League they could still end the most strange of seasons with three cups. (Reporting by Martyn Herman, editing by Pritha Sarkar)