Harry Charsley scored the only goal as Everton edged past Derby County 1-0 in Premier League 2 Division 1 at Pride Park.
The 20-year-old midfielder slid the ball home in the 29th minute to give the reigning champions their third successive victory.
An experienced Derby side could not find an equaliser, with Craig Forsyth glancing a header narrowly wide from a free-kick in the second half.
Everton are third in the table while Derby remain bottom, level with Manchester City on three points.
The Rams next travel to Manchester United on Friday, while Everton host second-placed Arsenal on Monday.
See: Derby report | Everton report