The result moved second-placed Liverpool four points ahead of Pep Guardiola’s team and kept them six points behind leaders Chelsea who beat Stoke City 4-2 earlier on Saturday.
The home side dominated the opening half after Wijnaldum leapt above City defender Aleksandar Kolarov to meet a pinpoint Adam Lallana cross and give Liverpool the advantage in the eight minute.
It was a goal of simplicity but quality and it highlighted the growing confidence of Lallana who was a creative threat down the left flank for much of the game.
Buoyed by the goal, Liverpool were first to the loose balls and looked sharper in their movement and crisper in their passing than a City team which was too often disjointed and lacking a clear purpose.
The return of Argentine Sergio Aguero to the City attack after a four-match suspension should have given the side a greater threat in attack but the striker was starved of service.
