Daniel Munoz gave visitors the lead in the first half when he returned home past Pickford from close range, but Toffee pulled out the level in the second term when Iliman Ndiai fined the house.
The Palace appeared to extend its unbeaten streak to 20 games, but after three minutes it increased the time, with clearance biasing against the grain and skewing backwards of the net to score three points for Everton.
Post-Coglu is under pressure after losing at St. James
Bruno Guimarès defeated the deadlock 58 minutes later before Nick Urtemado doubled the lead off the spot.
Since Postecoglou took over from Nuno Espirito Santo in September, Forest has not won in seven games in every tournament.
The Wolves late refused the first victory of the season
Elsewhere, the Wolverhampton Wanderers were denied their first Premier League victory this season after Brighton and Hove Albion scored a 1-1 draw at Molyneu Stadium.
The host took the lead during the opening period when Marshall Munetti’s thunderous volley was turned over by Bert Welbruggen to the crossbar before rebounding from the Brighton Keeper and rebounding behind the net.
However, in the two-week run, their minds were slowed down as Jean Paul Ben Hecke mounted the header home in the 86th minute.
The villa continues to win
Aston Villa continued its impressive turnaround with Doniel Maren’s braces garnering a 2-1 victory over Burnley at Villa Park.
The Dutch gave the advantage of 2-0 on either side of the interval, meaning that Leslie Ugochukw’s late header was merely comforting.
Unai Emery’s team did not win the opening of six games of the season in all competitions, but now they have won the final four games.
