Aaron Lennon was on target after 23 minutes while Ross Barkley tucked away two late penalties although Everton should have won more comfortably against Newcastle United, being denied by the woodwork three times in six second-half minutes.
Everton sealed their place in the FA Cup fifth round thanks to goals from Arouna Kone, Aaron Lennon and Ross Barkley.
Everton F.C. remain 11th, nine points below Mauricio Pochettino's Tottenham Hot Spur F.C., who squandered an opportunity to re-establish a five-point lead over fifth-place Manchester United.
