Ryan Gravenberch opened the scoring for Liverpool in the 10th minute, followed by Hugo Ekitike's goal in the 29th minute.
Everton's Idrissa Gueye pulled one back in the 58th minute, capitalising on a lacklustre second-half performance from Liverpool.
Despite Everton finishing strongly, they were unable to find an equaliser, extending David Moyes' winless streak at Anfield to 23 attempts.
The win maintained Liverpool's strong position at the top of the table, though their habit of conceding from a 2-0 lead highlighted ongoing adjustments for Arne Slot's side.