Fresh from consecutive home wins over Wolves and Manchester United in their battle for a European place, Albion presumably would have been high on confidence.
But they got off to the worst start possible with Abdoulaye Doucouré scoring within 40 seconds after the hosts fell asleep at the back.
Brighton looked for an instant response but struggled to find cohesion in the forward areas.
Everton were a constant threat on the counter attack and caught Brighton napping again on the half hour mark. The lively Dwight McNeil was given far too much time and space to pick out a cross to an unmarked Doucouré who made it 2-0 with a fine volley.
Roberto De Zerbi and his side – as well as the fans – were shell-shocked and things quickly got worse when McNeil’s cross found its way in via Jason Steele’s back leg.
Steele redeemed himself with a great save to keep the scoreline down and leave his side with a fighting chance of a comeback.
De Zerbi made four half-time changes, with Evan Ferguson, Solly March, Julio Enciso and Levi Colwill brought on to spark a fight-back. Danny Welbeck, Deniz Undav, Facundo Buonanotte and Adam Webster were the players to make-way.
The substitutes made an instant impact, with Brighton suddenly looking dangerous in the forward areas. Evan Ferguson and Alexis Mac Allister both hit the bar as Albion threw men forward but Everton’s defence held firm.
Albion were always going to be light on numbers at the back – and susceptible to a counter attack – and they conceded a fourth when McNeil rounded Steele and walked the ball into the net.
With the game well and truly won, Everton’s impenetrable defensive was breached in comical fashion when Alexis Mac Allister unknowingly deflected the ball into the net when Mitoma hit the post.
Brighton were unable to find another goal and the game seemed to be petering out until McNeil broke clear of the defence and fired a superb strike into the top corner for 5-1.
After a dreadful evening – where they were a mess defensively – Brighton will have to pick themselves back up quickly for a trip to title-chasing Arsenal next weekend. Here is how we rated the players.
5. Adam Webster: 3
Stood off McNeil and gave him too much space to pick out a cross for second goal. Some important defending at key moments but not good enough overall (Photo by Steve Bardens/Getty Images) Photo: Steve Bardens
6. Pervis Estupiñán: 3
Plenty of huff and puff but no end product today. Not great defensively either. (Photo by Mike Hewitt/Getty Images) Photo: Mike Hewitt
7. Pascal Groß: 4
Last weekend's two goal hero struggled to make a similar impact this evening. Another player who wasn't himself and looked leggy. One positive was his cross that led to Brighton's only goal. (Photo by Charlie Crowhurst/Getty Images) Photo: Charlie Crowhurst
8. Alexis Mac Allister: 4:
Very sloppy in the first-half as Everton dominated the midfield. Lost ball carelessly too many times. Came inches away with a flicked header onto the crossbar. Comical goal for 4-1. (Photo by Charlie Crowhurst/Getty Images) Photo: Charlie Crowhurst