After a goalless first leg and then tense first half on the night, Palace took the lead with 20 minutes left when Zaha sent a diving header into the net.
The Manchester United-bound winger sealed the Eagles' place in the final with two minutes on the clock left by turning in the area and lashing a shot off the underside of the crossbar.
Below, Sports Mole picks the bones out of a surprising victory for Ian Holloway's side.
On target 6
On target 5
Was the result fair?
Yes. After a cagey first half Palace did look more dangerous in the second and eventually were rewarded when Zaha dove in to head home. Brighton didn't really respond in the way that was expected and in the end it was quite a comfortable victory for Palace.
The Seagulls went into this match on a 10-match unbeaten streak but they never really got going tonight in front of an expectant sell-out crowd. At Selhurst Park in the first leg Gus Poyet's side were out of the traps instantly but today they couldn't get out of second gear.
A near-perfect visitors' display from Holloway's men. They stifled Brighton in the first half and then became increasingly dangerous on the counter-attack. Jonathan Williams should have put them ahead soon after the interval but his blushes were spared when Zaha took over in the final 20 minutes. Defensively, they almost paid for a brief slip in concentration midway through the second half when Brighton substitute Ashley Barnes first hit the bar before having a header cleared off the line by Dean Moxey.
Sports Mole's man of the match
Dean Moxey: Many will give Zaha the man-of-the-match accolade but he had a torrid first half before showing off his potential that has earned him a £15m move to Manchester United in the second. Palace's left-back Moxey is our man of the match tonight. He dealt with the threat of Will Buckley throughout and also cleared that Barnes header off the line minutes before Zaha's opener.
Has to go to Williams for his glaring miss soon after half time. The young Welshman had no-one challenging him but still drilled it just wide of the goal.
A solid, professional performance from Mark Clattenburg. He awarded bookings at the right time but did miss one clear penalty for Palace when Mile Jedinak was hauled over in the box.
Brighton: Not a lot. Brighton's season is over and it's a long summer ahead for Poyet.
Palace: Holloway has two weeks to prepare for the Wembley final against Watford on May 27.