The meeting, which took place at the Goodison Park stadium in Liverpool, ended with a score of 2: 2.
Michael Keane and Dominic Calvert-Lewin scored for the hosts.
Sadio Mane and Mohammed Salah scored among the guests.
Everton tops the Premier League standings with 13 points after five games.
Liverpool are in second position with ten points.
Earlier, the ex-Liverpool footballer put up for auction a medal for winning the 2004/05 Champions League.