The hosting Canaries broke the deadlock six minutes before the break when Irish midfielder Wes Hoolahan turned in a corner from Andrew Crofts. However, Newcastle felt aggrieved by the goal as they claimed that a corner should never have been awarded.
Just before the hour-mark Norwich went back in front courtesy of Grant Holt, who headed his 50th league goal for the club from close range.
Holt's strike partner Steve Morison then found the net in the 63rd by heading in a cross from Crofts.
Despite their numerical disadvantage Newcastle managed to pull a goal back through Ba, who collected possession from Shola Ameobi before scoring from the edge of the area.
Holt sealed the points for Norwich with another headed goal in the 82nd minute; on this occasion Bradley Johnson was the provider.