The Ivorian went on a mazy run past several Huddersfield defenders, before slamming a ferocious strike into the top corner.
The goal was enough to give Palace their first win since the opening day.
Zaha had been a doubt before the match due to a groin injury, but he recovered sufficiently to play a key role in the match.
Teammmate Kouyate said: "It was an unbelievable goal, yes.
It was a solo goal. We know Wilf is an amazing player, a very, very good player, but today - what a goal for him. He's very important for us."
The win leaves Palace in 11th, while Huddersfield are currently languishing in 17th.