James McArthur put the hosts ahead in the first minute before Leighton Baines levelled matters with a well-taken penalty five minutes later.
The Cote d’Ivoire international tapped home Joel Ward’s cross to restore the Eagles’ lead in the 35th minute but Senegal international Oumar Niasse drew the Toffees level ten minutes later to end an enthralling first half.
There were no further goals in the second half as both teams settled for a share of the spoils, and the ex-Manchester United striker is crestfallen Roy Hodgson's side could not hold on to their leads.
Disappointed to not get the win but we’ll take the point. Happy to get another goal & great to have my bro @chrisbenteke back. Thanks for the support #CPFC pic.twitter.com/rqPLcMdP3p — Wilfried Zaha (@wilfriedzaha) November 18, 2017
Zaha has been in great form since his return from an ankle injury and has now scored three goals in five games in the English Premier League.
Crystal Palace, however, remain bottom of the English top-flight standings, having garnered just five points from 12 games played so far this term.