The 20-year old attacker netted a double as the Eagles bounced back from a 0-0 draw at home in the first leg to defeat Brighton & Hove Albion 2-0 at the Amex Stadium to progress to the Premier League promotion decider with Watford.
Zaha, who will already be playing in the top flight with Manchester United next season, was the hero for Palace and admitted it was a dream come true to be heading to Wembley with the South London club.
"I can't explain it. No words can express how I feel," he told Sky Sports.
"I have played for Palace for ten years. I am just happy I scored and finished strong for the club.
"We go to Wembley now and that's a dream."