City upped the pressure and absolutely peppered the Everton goal with shots for a short spell after the half hour, but the Toffees somehow kept out David Silva, Vincent Kompany and Mario Balotelli.
And City made the points safe on the stroke of half-time when Vincent Kompany powered a header past goalkeeper David James from Martin Petrov's corner.
Carlos Tevez and David Silva struck in the first half with Vincent Kompany and an own goal by Newcastle defender James Perch completing a resounding victory for Robert Mancini's team.