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.