Victory moves Everton up to ninth in the table, while Brighton are 12th - enjoying a three-point cushion between themselves and West Ham United in 13th.
Everton's strong start to the second half proved key as long-serving Toffees right-back Coleman restored a lead Richarlison would enhance 13 minutes from time.
What does it mean?
Everton are now ninth in the table but there's more optimism among the supporters because in Marco Silva, the club has a manager that will try to play attacking football. While Brighton have played well lately, they have not played well in their away games.
With the game level on 50 minutes after goals from Richarlison and then Lewis Dunk, the 30-year-old received the ball on the edge of the box before setting himself and drilling a low hard shot beyond Mat Ryan in goal.
Perhaps the most encouraging aspect is that only Arsenal have prevented them from scoring, although that is not so surprising given that Silva's attacking approach was already evident with Hull and Watford and now he has much better players.
Everton defender Seamus Coleman says he was frustrated at not having scored since January 2017, and says that his celebration was just his usual "going a little bit mad".
"It was a frustrating time to be out and this season I've had a few niggles".
Brighton ended the game with 10 men as Alireza Jahanbakhsh had to come off injured in the final minutes after Brighton had used all three of their substitutions.
- francis millea (@francis_millea) November 3, 2018That's a great win for Everton against a tough Brighton side. In five away games, the Seagulls have won only one game and picked up four points.
- Everton attacker Richarlison has netted six goals in nine Premier League appearances in 2018-2019, one more than his total haul from 38 games last season.
Silva has brought in a lot of new faces to the squad since taking charge and Everton fans are excited by the addition of André Gomes to the midfield.