Spaniard Negredo and his Argentine strike partner Aguero scored one apiece as City came from behind in the early kickoff to go second in the table.
Romelu Lukaku, on loan from Chelsea, had given Everton a 16th-minute lead before City hit back, going some way to ease the disappointment of their 3-1 home defeat by Bayern in the Champions League on Wednesday.
Everton's frustrating afternoon was complete when Tim Howard was credited with City's third goal after 69 minutes after the keeper had tipped Aguero's penalty on to the post, only for the ball to ricochet off his head and into the net.
Everton's first defeat of the season ended a run of three league wins in a row and Roberto Martinez's side slipped to fifth in the table on 12 points, one behind City and three adrift of leaders Arsenal.
Third-placed Liverpool could return to the top when they play Crystal Palace at home later on Saturday and champions Manchester United bid to avoid a third successive defeat when they travel to Sunderland in the late kickoff.