Ashley Young's 84th-minute own goal rescued a point for Brighton as Everton were denied back-to-back Premier League victories in a 1-1 draw at Goodison Park.
The hosts raced into a seventh-minute lead when Vitaliy Mykolenko scored just his second goal for the club before Lewis Dunk's sublime volley from Pascal Gross' free-kick was ruled offside by VAR Michael Oliver.
But Brighton were convert their possessional dominance into a late draw as Kaoru Mitoma's cross deflected off the unfortunate Young and looped over Jordan Pickford with six minutes of normal time remaining.
The result means Everton stay in 15th place while Brighton move up to sixth in the Premier League table but have now gone five games without a win.
Gross said: "We were the better team for the whole 90 minutes. We tried to play active football. We came here to play football. They played for a result from the first minute. We approached the game differently. I'm proud of the boys for keeping going."
- How the teams lined up | Match stats
- Premier League table | Watch free Premier League highlights
- Get Sky Sports | Stream the biggest moments on NOW
Everton frustrated by cruel late blow
Roberto De Zerbi failed to win any of his opening five games after taking over from Graham Potter just over a year ago, and while he has now repeated that inauspicious start to his time in England, the manner of his side's late draw will fill him with satisfaction. In truth, it was a final outcome that was merited.
Much-needed positivity is sweeping into the blue half of Merseyside and for Everton, things have started to come together at last in what is expected to be the final full season of Goodison Park.
"The mentality is growing all the time, that hardy edge," Sean Dyche said afterwards. "I like the way the players are opening their minds to the different ways they can affect a game. Barring a very unfortunate moment, I think we see the game through 1-0.
"The crowd were excellent today; they see a team giving everything. That is the minimum. It is tough to ask more of these players after three games in six days."
When Dyche reflects on the game he may well see it more as two points dropped as he felt his side should have had a second-half penalty while still leading when Dominic Calvert-Lewin was wrestled to the ground by Jan Paul van Hecke.
"I know, because I was a centre-half, he (Van Hecke) is the wrong side of him. I think you do things like that because you have that moment when you think 'He is in'," Dyche added.
"That is a really important call and it went against us but I don't know how it went against us because I thought it was obvious.
"I'm bound to say that, but when people see it I'll be surprised if they didn't think there was certainly a big suggestion of that being wrong. I'm not saying it is an absolute but it is a long way to being a decision which should have been given in my opinion."
It says a lot about how perspectives have changed in the last few weeks that Everton were disappointed with a draw against a team who finished sixth last season, but in the see-saw world of the Premier League the Merseysiders remain upwardly mobile while Brighton manager De Zerbi is still trying to work out why his team cannot convert possession into points.
The Seagulls' last top-flight victory on September 24 lifted them to third in the table on 15 points; the same weekend Everton won their first game to move out of the bottom three with four points.
Brighton, who have taken just three points from the last 15 available, enjoyed 90 per cent possession in the opening 10 minutes but Everton had already managed three shots on target, two of those from Mykolenko in the attack which led to his goal.
The other was a volley from Abdoulaye Doucoure, fresh from signing a new contract, which was parried by Bart Verbruggen who had replaced Jason Steele in goal as one of five changes.
Mykolenko showed a proficiency in front of goal not seen before as his left-foot strike from Dwight McNeil's cross was parried by Verbruggen only for the defender to lash home only his second goal for the club with his weaker right foot in the seventh minute.
The Ukraine international last found the net towards the end of his debut season in May 2022.
With the pattern of the game firmly established - Brighton ended the game with 80 per cent possession - it was set up for an Everton rearguard action and that played right into their hands, with James Tarkowski and Jarrad Branthwaite again excellent against Evan Ferguson, with Mykolenko providing admirable support.
Everton looked to have been breached by Dunk's brilliant volleyed equaliser at the far post from Gross's 15th-minute free-kick only for VAR to intervene as the Seagulls began their long dominance of the ball, although they remained uncharacteristically careless with it and that offered Everton encouragement.
As a result, Calvert-Lewin found himself in a two-on-two but dragged a shot wide with Doucoure in support, while Joel Veltman's tangle with McNeil in the penalty area was deemed accidental by referee Tim Robinson.
Joao Pedro's second-half introduction for Adam Lallana gave Brighton a better option going forward but even then they did not properly threaten, with Pickford's first genuine save coming in the 55th minute when he tipped over Dunk's free-kick.
But he could not reach the wickedly dipping ball which sailed over him from Mitoma via Young.
Dyche delighted by Everton work ethic
Everton boss Sean Dyche:
"I'm delighted. Three games in six days, the work ethic is good, we are tactically very good and improving all the time. It is a blow to concede; we kept them quiet.
"Brighton are a good side; they use the ball well and don't lose faith in it. We should have done better on the counter at times; in saying that we had two refereeing decisions on the edge of their box.
"I don't know what is going on anymore to be honest. They should go for us; on another day, I'd hope we get them.
"They are a very good outfit. Obviously we are very unfortunate with a massive deflection after them not having many chances at all. I thought the tactical side of the game was fantastic from the players."
De Zerbi: We aren't in our best moment
Brighton boss Roberto De Zerbi:
"The result is fair as we played a good game but not enough to win it. We didn't shoot enough to win the game.
"We kept the ball and played well until the final third. We had chances to shoot more. It's not the best moment for us and we're not playing with the same quality we've played in the past.
"That can happen in football and in a season, but I still think we played well.
"We are a great team, and we have to be strong in this moment with the injuries. We have to move on and be focused on the next game in Amsterdam.
"We want to win for sure and most importantly to play with energy, with attitude and with the right spirit."
Another step in right direction for Everton
Sky Sports' Ben Grounds:
"Mykolenko looked like being an unlikely match-winner with his first goal in 18 months before Mitoma's cross took a freakish deflection off the Toffees' other full-back with six minutes remaining.
"Having taken the lead, Everton had done a good job of keeping the visitors at bay - assisted by VAR ruling out Dunk's equaliser for offside and also a good save by Pickford to deny the Seagulls captain - and Dyche's side looked well set for their first back-to-back Premier League wins in 13 months.
"Despite the late disappointment, the body language of Pickford and Tarkowski at full-time - and the forlorn Young on the sidelines - in some ways tells you how the perceptions are shifting at Everton.
"Last season, they were thrashed 4-1 in the corresponding fixture, but after Brighton's fortuitous leveller it was Everton who responded positively to force De Zerbi into bringing on Igor Julio to preserve a point.
"After back-to-back seasons ended with narrow escapes from relegation, this is effectively the first time during that spell where the team and fans can start looking up rather than over their shoulders. While Dyche is not getting carried away, this point is another step in the right direction."
Player of the match - Abdoulaye Doucoure
Doucoure was training away from the first-team squad in the final weeks of Frank Lampard's tenure following a falling out but the Mali international has flourished under Dyche this year.
He scored five goals in the second half of last season and has struck three times this term, including in wins over Brentford and Bournemouth.
This season, he has already been instrumental besides his goal involvements, with his touches and runs into the box, dribbles from midfield and distance covered more than any other team-mate.
It is no wonder Dyche has been so eager for Doucoure to commit his future to the club this week. He might have capped his new contract with an early goal but it was his sheer work off the ball which ensured Everton made Brighton work so hard to earn their point.
Seagulls not keeping it clean - Opta stats
- Brighton became the first team to both score and concede a goal in each of their first 11 games of an English top-flight campaign since Tottenham Hotspur in 1988-89.
- Everton have picked up 10 points in their last six Premier League games (W3 D1 L2), as many as their previous 14 beforehand (W2 D4 L8).
- Brighton had 79.8% possession against Everton but recorded just seven shots; before this, the highest amount of possession a side had managed in a Premier League game on record (from 2003-04) while having a maximum of seven shots was 72.3% by Chelsea against Nottingham Forest in January last season.
- Aged 38 years and 118 days, Everton's Ashley Young was the fourth-oldest player to score an own goal in the Premier League, and oldest since Phil Jagielka against Leeds United in April 2021 (38y 229d).
What's next?
Everton travel to Crystal Palace next Saturday, kick-off 3pm. After the international break, they host Manchester United on November 26 live on Sky Sports, kick-off 4.30pm.
Brighton visit Ajax in the Europa League on Thursday; kick-off 5.45pm. They then host Sheffield United on November 12, kick-off 2pm.