MS Dhoni's cameo in vain as five-time champions dealt thrid loss but hold on to third place in the standings
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 semifinal 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 semifinal.
Manchester United v Chelsea
Arsenal v Manchester City
Matches will be played at Wembley on July 18-19
MS Dhoni's cameo in vain as five-time champions dealt thrid loss but hold on to third place in the standings
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All competent authorities must work together and coordinate to expedite possible means of support