Midfielder Fabian Delph put City ahead after 22 minutes, his speculative strike squirming under Palace keeper Wayne Hennessey.
Aguero doubled the lead just before halftime when his shot from 30 metres hit defender Scott Dann’s head and flew past the helpless Hennessey into the net.
The Argentine forward struck again from close range after 68 minutes following a fine one-touch passing move and a perfect cross from Kevin de Bruyne before David Silva completed the rout.
City manager Manuel Pellegrini was pleased with his players who drew at home with Everton on Wednesday.
“We had to refresh the team as we had less than 72 hours and that is not enough to recover,” he told the BBC.
“The first half, the two goals gave us more space as they’ve had to go for the draw. That allowed us to use that space and score two more.”
Palace manager Alan Pardew is planning to keep faith with Hennessey, who also made a costly mistake in the 1-0 defeat at Aston Villa on Tuesday.
“Wayne is going to have to show me this week in training. A mistake at Villa, he needed to respond today and made another mistake,” Pardew said.
“The ball is in his court to keep out the other two goalkeepers but I need to see it in training, I need to see a reaction from him. I will give him that chance because he deserves it.”