City, who are the holders of the competition, fell 1-0 behind after just six minutes when Rolando Aarons finished from inside the box and that goal was the difference between the two sides at the interval.
City responded in the second period, but it was Newcastle that scored again after 75 minutes, with Moussa Sissoko's effort securing the Magpies a surprise spot in the next round.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
MAN CITY: Caballero; Sagna, Demichelis, Mangala, Kolarov; Milner, Toure, Fernandinho, Silva; Jovetic, Dzeko
NEWCASTLE: Elliot; Janmaat, Coloccini, Dummett, Haidara; R Taylor, Abeid, Colback; Obertan, Armstrong, Aarons