The Brazil forward's fifth Premier League goal of the season put Marco Silva's men ahead after 26 minutes but their advantage was short-lived – Lewis Dunk heading the Brighton equaliser seven minutes later.
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.
Victory moves Everton up to ninth in the table, while Brighton are 12th – enjoying a three-point cushion between themselves and West Ham in 13th
Gylfi Sigurdsson made a horrible hash of his shot on the end of Coleman's 11th-minute cutback.
The Iceland midfielder more than made up for that error by driving the hosts forward on the break from a Brighton corner, exchanging passes with Bernard and slipping a deft pass behind the visiting defence for Richarlison to gleefully smash home.
Everton remained in the ascendancy, with Alireza Jahanbakhsh fortunate not to be penalised for a clumsy challenge on Lucas Digne in the box, but they levelled when Dunk climbed above Zouma to power past Jordan Pickford.
Idrissa Gueye drilled a 20-yard strike against the inside of the right post in the 48th minute, with Theo Walcott unable to covert Bernard's pacey cross from the loose ball.
Coleman found the precision his team-mates lacked a few moments later, driving beyond Mat Ryan from the edge of the box.
Dunk wrapped up an all-action outing in forgettable fashion when his woeful blind pass towards centre-back partner Shane Duffy was seized upon by Richarlison, who finished with aplomb from a tight angle after skipping away from Ryan.
What does it mean? Everton taking shape under Silva
Last weekend's narrow defeat against Manchester United certainly stands as a blip for the Merseyside club. They've now won four of their past five league games, with the creative talents of Sigurdsson and Bernard beginning to gel irresistibly and Andre Gomes bringing a steadying hand in midfield. Brighton's run of three consecutive 1-0 wins has come to an end.
Coleman goes against the grain
Everton's skipper had not found the net since before a horrific leg break while playing for Republic of Ireland against Wales last March. It should have been a moment of unbridled joy but Coleman, who has struggled for form and fitness this term, decided it was time to make a point as he tore off furiously towards the Gwladys Street End, cupping his ears. Perhaps the 30-year-old should have given himself time to savour the moment, but his passion for the club he has represented for the past 11 years clearly remains undimmed.
Jahanbakhsh still finding his feet
Brighton's recent flurry of low-scoring wins showed plenty of admirable qualities but a slight over-reliance on evergreen striker Glenn Murray. It is time for Jahanbakhsh to relocate the form that saw him finish last season as the top scorer in the Eredivisie and persuaded Brighton to pay AZ £17million. Pickford pushed his late attempt over and the Iran forward remains without a Premier League goal in four starts and six substitute appearances.
Key Opta facts
- Everton have enjoyed four wins in their last five Premier League games (L1), as many victories as they managed in their previous 14 in the competition.
- Brighton have never won away at Everton in any competition, drawing two and losing five of their seven visits.
- Brighton have managed just one win in their last 19 Premier League away games, drawing five and losing 13.
- Everton attacker Richarlison has netted six goals in nine Premier League appearances in 2018-19, one more than his total haul from 38 games last season.
- All 11 of Everton forward Richarlison’s Premier League goals have come under manager Marco Silva (11 in 33 apps under Silva, 0 in 14 apps under Javi Gracia).