Dominic Calvert-Lewin put Everton ahead on 16 minutes, heading in Gylfi Sigurdsson’s cross at the far post to become the first Toffees player to score in their four opening matches of a Premier League campaign.
Brighton equalised four minutes before half-time when Neal Maupay reacted quickest to cross dropped by Jordan Pickford. But Yerry Mina restored Everton's lead before the break, heading in Rodriguez’s free-kick.
After the break, Rodriguez scored twice to put the match beyond Brighton, both times converting at the far post from a left-wing cross.
Yves Bissouma’s magnificent long-range volley in stoppage time was a late consolation for Brighton, who drop to 14th.
Everton are top with four wins from four.
Everton: 17 Oct v Liverpool (H)
Brighton: 17 Oct v Crystal Palace (A)