Ashley Young's unfortunate own goal allowed Brighton to salvage a late Premier League point at Everton.
The visitors were being contained by a resolute Everton backline before Kaoru Mitoma's cross from the left on 83 minutes took a deflection off Young and looped in over Jordan Pickford.
It was a cruel finish to the game for Sean Dyche's side, who had snuffed out the danger for most of the game but were unable to cling on to the lead given them by Vitaliy Mykolenko's early goal.
Ukraine full-back Mykolenko fired home a strike which deflected in off Lewis Dunk at the near post after only seven minutes, after the visitors could not clear his initial effort.
Brighton captain Dunk thought he had made amends with a stunning volley from Pascal Gross' free-kick, but the effort was ruled out by VAR for offside.
The visiting centre-half also forced Jordan Pickford into a fine save in the second period with a dipping free-kick, before Young's unlucky intervention gave them a draw.
Follow live coverage of Saturday's Premier LeagueHow did you rate Everton's performance? Have your say hereWhat did you make of Brighton's display? Send us your views hereEverton heading in right direction
Dyche will be left irritated that his side could not cling on to all three points, but this was another promising performance from an Everton side that were so hapless at the start of the season.
The manager was adamant they were heading in the right direction, despite losing four of their first five games - drawing the other at Sheffield United - and scoring only two goals.
And Everton have indeed turned the corner, suffering defeat in only two their past eight games and also progressing to the Carabao Cup quarter-finals on Wednesday night.
The Toffees' trip to Brighton last season saw them claim arguably the most surprising result of the campaign as they came away with a thumping 5-1 victory, and this game back on home soil looked to be going in their favour too.
Mykolenko's early goal, reacting quickest after his first shot was kept out by Brighton goalkeeper Bart Verbruggen, put them on course for back-to-back league wins for the first time in 13 months.
They had only 20% possession but offered more of a goal threat and could have had more but Abdoulaye Doucoure, fresh off committing his future to the club until 2025, saw his thumping volley pushed away by Verbruggen.
James Garner curled a free-kick over and the imposing Dominic Calvert-Lewin dragged wide, while Dwight McNeil fired a low drive just wide in the second half.
The hosts managed to shackle Brighton's attacking threat with the colossal Jarrad Branthwaite subduing teenage striker Evan Ferguson, who failed to make an impact before being substituted in the second half.
But with time running out, the fleet-footed Mitoma turned right and left before his cross into the box struck Young's knee and sailed over Pickford almost in slow motion before nestling in the back of the net.
After a thrilling first season under Roberto de Zerbi in which they qualified for the Europa League, the Seagulls have hit a sticky patch this term, now winning just one of their last eight games in all competitions.
They have had injuries to key players such as Pervis Estupinan, Danny Welbeck and Solly March to deal with but their off-colour form will be of concern to the Italian manager.
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Everton
Squad number1Player namePickford
Squad number18Player nameYoung
Squad number6Player nameTarkowski
Squad number32Player nameBranthwaite
Squad number19Player nameMykolenko
Squad number11Player nameHarrison
Squad number37Player nameGarner
Squad number27Player nameGueye
Squad number7Player nameMcNeil
Squad number16Player nameDoucouré
Squad number9Player nameCalvert-Lewin
Squad number2Player namePatterson
Squad number14Player nameBeto
Brighton & Hove Albion
Squad number1Player nameVerbruggen
Squad number34Player nameVeltman
Squad number29Player namevan Hecke
Squad number5Player nameDunk
Squad number13Player nameGroß
Squad number14Player nameLallana
Squad number11Player nameGilmour
Squad number6Player nameMilner
Squad number24Player nameAdingra
Squad number28Player nameFerguson
Squad number22Player nameMitoma
Squad number3Player nameIgor Julio
Squad number8Player nameDahoud
Squad number9Player nameJoão Pedro
Squad number31Player nameAnsu Fati
Squad number40Player nameBuonanotte
Line-ups
Everton
Formation 4-4-1-1
1Pickford18YoungSubstituted forPattersonat 90'minutes6TarkowskiBooked at 81mins32BranthwaiteBooked at 77mins19Mykolenko11Harrison37Garner27GueyeBooked at 43mins7McNeil16DoucouréBooked at 54mins9Calvert-LewinSubstituted forGomes Betuncalat 90'minutesSubstitutes
2Patterson5Keane10Danjuma12Neves Virgínia14Gomes Betuncal22Godfrey28Ramalho Chermiti31Lonergan61DobbinBrighton
Formation 4-3-3
1Verbruggen34Veltman29van Hecke5DunkBooked at 23mins13Groß14LallanaSubstituted forJoão Pedroat 45'minutes11GilmourBooked at 20minsSubstituted forDahoudat 68'minutes6MilnerSubstituted forBuonanotteat 79'minutes24AdingraSubstituted fordos Santos de Pauloat 90'minutes28FergusonSubstituted forAnsu Fatiat 68'minutes22MitomaSubstitutes
3dos Santos de Paulo4Webster8Dahoud9João Pedro20Baleba23Steele31Ansu Fati40Buonanotte41HinshelwoodReferee:Tim Robinson
Attendance:38,683
Live Text
Match ends, Everton 1, Brighton and Hove Albion 1.
Second Half ends, Everton 1, Brighton and Hove Albion 1.
Corner, Brighton and Hove Albion. Conceded by Nathan Patterson.
Attempt saved. James Tarkowski (Everton) header from the centre of the box is saved in the top centre of the goal. Assisted by James Garner with a cross.
Substitution, Brighton and Hove Albion. Igor Julio replaces Simon Adingra.
Substitution, Everton. Nathan Patterson replaces Ashley Young.
Substitution, Everton. Beto replaces Dominic Calvert-Lewin.
Corner, Everton. Conceded by Joël Veltman.
Attempt blocked. Vitalii Mykolenko (Everton) left footed shot from outside the box is blocked. Assisted by James Tarkowski.
Attempt blocked. James Tarkowski (Everton) header from the left side of the six yard box is blocked. Assisted by Dwight McNeil with a cross.
Corner, Everton. Conceded by Pascal Groß.
Mahmoud Dahoud (Brighton and Hove Albion) wins a free kick in the defensive half.
Foul by Abdoulaye Doucouré (Everton).
Own Goal by Ashley Young, Everton. Everton 1, Brighton and Hove Albion 1.
James Tarkowski (Everton) is shown the yellow card for a bad foul.
Ansu Fati (Brighton and Hove Albion) wins a free kick on the left wing.
Foul by James Tarkowski (Everton).
Foul by Joël Veltman (Brighton and Hove Albion).
Dwight McNeil (Everton) wins a free kick in the defensive half.
Substitution, Brighton and Hove Albion. Facundo Buonanotte replaces James Milner.