Crystal Palace maintained the momentum, creating another chance when Ismaïla Sarr crossed the ball into the six-yard box, but Jean-Philippe Mateta was unable to connect with it.
The first half was marked by few clear-cut scoring opportunities for either team.
City's first notable chance came from a set piece, when Phil Foden curled a shot around the wall, but Dean Henderson saved it.
City's goal was inevitable, and Erling Haaland scored when he headed in Matheus Nunes' delivery from a corner kick.
Palace tried to mount a comeback after halftime, and Wharton hit the woodwork from outside the area.
Tijjani Reijnders came close to doubling City's lead with a shot that forced a one-handed save from Henderson, but City didn't need much time to secure the win.
Foden was instrumental in the victory, controlling the center of the pitch and scoring a goal with a shot into the bottom corner.
In the final stages, Crystal Palace made a substitution, replacing Nathaniel Clyne with Christantus Uche in an attempt to find a late equalizer.
