The Cote d'Ivoire international canceled out Mark Noble's first-half effort in the 76th minute as the Eagles stretched their unbeaten run to four games across all competitions.
The goal saved Roy Hodgson's men from a disappointing home loss after managing 25 shots - 19 more than their visitors - at Selhurst Park.
The point earned moved Crystal Palace five points adrift of the top half of the Premier League as they currently sit 13th with 27 points from 26 matches.
And Zaha who returned to action after serving a one-game ban for receiving two yellow cards against Southampton a fortnight ago hailed the team's performance and urged them to keep soaring.
"God is the greatest. Should have won today but got to take the point and move forward. Great performance from the team," Zaha tweeted.