Kaoru Mitoma opened the scoring via James Tarkowski’s legs inside a quarter of an hour but a seven-minute spell after half-time proved the nadir for Everton as the Seagulls scored three times.
Irish teenager Evan Ferguson’s neat finish doubled Brighton’s lead after 51 minutes and Everton’s defence were at sixes and sevens as Solly March and then Pascal Gross helped the visitors move out of sight.
By this point Everton’s fans were streaming towards the exits and not even Demarai Gray’s added-time penalty could placate those who remained, with chants of ‘sack the board’ ringing around the stadium.
Everton were booed off the field for the second home match in a row and, while they remain one point above the Premier League relegation zone, all four teams below them have a game in hand.
“I’m happy for Evan, he played a fantastic game,” the Brighton manager said after the win.
“He has big potential and I think he can help us in the second part of the season. With Danny Welbeck, he can be very important as our strikers. Evan could become a great striker because he has all the qualities, both physical and technical.
“It was a mature performance by Evan. My job is to give him and the other young players the possibility to play. Sarmiento played a good game too and I want to progress with young players."
Ferguson is now in line to start again in Saturday's FA Cup tie away to Middlesbrough and potentially stay in the side for their next league game, against Liverpool.
He added: “In the first half I didn’t like the quality of our play in defensive spaces, but I can understand this, every Premier League game is difficult.
“But we asked more of ourselves and the second half was amazing, there was a different quality to our play – we played well. We played with more energy and scored more goals, I am only sad because of their goal. Their goal changed nothing today, but it could [do so] at the end of the season. But it is an important result and I am happy."