Championship (second tier) side Rotherham, who haven't made it through to the fourth round of the competition since 2001-02, kept their composure early on as Fulham controlled the play.
The former Fulham footballer was one of the most gifted playmakers England ever produced.
Top-class goals from Bernardo Silva and Sergio Aguero took Manchester City back to the top of the Premier League in a 2-0 win over Fulham at Craven Cottage on Saturday.