City moved a point ahead of Liverpool, which hosts Tottenham on Sunday but will have played a game more than Pep Guardiolas defending champions.
It is little wonder Fulham is next-from-last and facing relegation given the sloppiness of the defending before both City goals.
A misplaced, casual clearance by Timothy Fosu-Mensah in the fifth minute was seized on by Kevin de Bruyne. Aguero received the ball from the Belgian before he teed up Bernardo Silva to strike low into the net.
Fulham was so ineffective on the ball that, when the hosts finally strung passes together in the 15th minute, there were ironic cheers around Craven Cottage.
It was a brief intermission from the City supremacy.
Fulham defender Joe Bryan even helped City with its second goal in the 27th minute.