The Magpies took the lead in the sixth minute when Fernandinho's mistake deep into his own half allowed 18-year-old Rolando Aarons to pick up the ball before confidently slotting it past goalkeeper Willy Caballero.
In the 21st minute, however, the hosts had a great chance to pull themselves level when substitute Samir Nasri lashed a cross into the box, Stevan Jovetic at hand to seemingly bundle his effort into the bottom corner. However, Newcastle keeper Rob Elliott pulled off a smart save to deny the Montenegrin striker.
More action was to come as Fabricio Coloccini sliced a James Milner ball against his own post just before the half-hour mark, while Paul Dummett forced a reflex leg stop from Caballero at the other end a few minutes later.
The French midfielder was at the centre of the action again when he was brought down by Aleksandar Kolarov midway through the second half, but the referee waved play on.
City piled forward in a bid to find a consolation at the very least, but Newcastle were able to see the game off in efficient fashion to shock the holders and advance to the next round of the League Cup.