Jarrad Branthwaite’s 94th minute equaliser salvaged a 2-2 draw for Everton against Tottenham that dragged the Toffees out of the relegation zone on Saturday.
Richarlison’s double on his return to Goodison Park looked set to take Spurs level on points with third-placed Arsenal.
But Ange Postecoglou’s men were denied at the death as Branthwaite met a free-kick at the far post to boost Everton’s chances of survival.
Tottenham remain in fourth but could be leapfrogged by Aston Villa, when they travel to struggling Sheffield United later on Saturday.
“It’s obviously never going to be an easy game here. You have to deal with a fair bit but most of the time we handled it ok,” said Postecoglou. “Unfortunately we couldn’t hold out.”
Richarlison had scored just one Premier League goal for Tottenham between his £60 million ($76 million) move in July 2022 and December 2023.
But he has now struck nine times in Tottenham’s last eight Premier League games, with his hot form timely in the absence of Son Heung-min at the Asian Cup.
The opener arrived after just four minutes as Destiny Udogie’s run to the by-line was not tracked and the Italian’s driven cross was brilliantly swept in first time by Richarlison.
The 26-year-old was applauded by the Everton support after he refused to celebrate his goals and even raised a hand in apology to the home support.
Everton’s fans were less forgiving of the Premier League, as it is due to a 10-point deduction for breaches of financial rules at the end of the 2021/22 season, that they find themselves in a battle for survival.
Further punishment could be on the cards for Everton, who face another charge of exceeding profit and sustainability limits for last season.
Placards and chants taking aim at the league’s hierarchy took place before kick-off and in the 10th minute.
Everton’s appeal against the toughest sporting sanction in Premier League history took place this week with a verdict expected by the middle of the month.
• ’Deserved’ point for Everton –
If they are not successful in clawing back at least some of their lost points, they desperately need a change of fortunes on the pitch.
Sean Dyche’s men have failed to win in six Premier League games and moved out of the relegation zone on goal difference, having played two more games than Luton in 18th.
“We deserved at least an equaliser if not take all three (points)”, said Dyche.
Everton did rally after a poor start and levelled as their tactic to target Spurs goalkeeper Guglielmo Vicario from corners paid off.
The Italian thought he was fouled for Manchester City’s late winner in Tottenham’s FA Cup exit last weekend and was again not strong enough in coming off his line.
Jack Harrison was backing into Vicario and then on hand to turn in Dominic Calvert-Lewin’s header towards goal.
“It seems to be that maybe just with us referees are reluctant to call these now,” added Postecoglou.
Just as Everton were building up a head of steam, Richarlison silenced Goodison once more with a stunning strike from outside the box that curled into the top corner.
Tottenham controlled the game better in the second period and were made to rue not taking their chances to put the game to bed.
Jordan Pickford turned behind Pedro Porro’s blistering strike and then denied Richarlison his hat-trick from close range.
The England number one’s saves proved to be worth a crucial point as Tottenham again failed to deal with an Everton set-piece in stoppage time.
Cristian Romero could only head James Garner’s free-kick towards his own goal and Branthwaite bundled the ball home despite the best efforts of Vicario.