The two sides were level 0-0 after Friday's first leg and it took until the 69th minute of the second leg for the visitors to break the deadlock.
Zaha, who is joining Premier League champions Manchester United in July, sent Palace a step closer to joining him in the top flight with a header from close range after a superb cross from substitute Yannick Bolasie.
The Ivory Coast-born forward made sure of the win with a fine left-footed strike into the roof of the net two minutes from time.
Palace, who finished fifth this season behind fourth-placed Brighton, are seeking a return to the Premier League for the first time since they were relegated in 2005, while manager Ian Holloway last managed in the top flight with Blackpool in 2011.
Watford booked their place in the May 27 final at Wembley on Sunday when they beat Leicester City 3-1 on the day for a 3-2 aggregate victory.
Champions Cardiff City and runners-up Hull City won automatic promotion to the Premier League.
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