Edin Dzeko nearly put the visitors ahead with less than three minutes on the clock, but Tim Krul denied the Bosnian striker after he was picked out with a ball over the top.
Neither side could create any real openings, although Newcastle were beginning to force their opponents into making a few errors as the half progressed at St James' Park.
Seven minutes before the interval City did strike against the run of play, though, and it was David Silva who made the breakthrough with a drilled finish past Krul following a flicked pass from Dzeko into his path.
There was an early scare for the Citizens in the second half as they struggled to deal with a corner whipped into the box, but the danger was soon cleared with their lead still intact.
Stevan Jovetic came close to adding a second for his side on 55 minutes when he struck the ball from 25-yards out, only to see his attempt fly wide of the target.
Another chance soon followed for City, this time for Dzeko who headed over from close range, while Yaya Toure's free kick sailed inches over the bar.
The missed opportunities almost proved costly when Ayoze Perez broke free from the opposition defence before getting a shot away at goal which was deflected narrowly wide.
Substitute Sergio Aguero made sure of the points in added time, however, with his finish from close range when he pounced on a rebound ahead of Fabricio Coloccini.
