Zaha grabbed the opening goal in the 69th minute when he powerfully headed home sub Yannick Bolasie's pin-point left wing cross to line-up a Wembley date with Watford on May 27 for a place in the Premier League.
The second leg looked to be heading for extra-time with a repeat of the first-leg 0-0 scoreline on the cards, before Bolasie's fine ball in was converted by the diving Manchester United-bound Zaha.
And with two minutes remaining Zaha turned Gordon Greer in the box and crashed home a shot in off the crossbar to secure their date at Wembley.
It means Ian Holloway's Palace, who only secured their place in the top six on the final day of the season following a dismal run of form, will play Gianfranco Zola's Watford in the final in a fortnight.
It was a different story in the first half for Zaha, who struggled to make an impact and became frustrated at some of the close attention he was receiving from Brighton's defenders.
Instead the Seagulls bossed the early stages with Julian Speroni having to keep out Will Buckley's drive before David Lopez's shot was deflected narrowly over.
Former England defender Matt Upson headed Andrea Orlandi's corner wide, Dean Hammond was also off target with a fierce, low drive and Orlandi's volley was straight at Speroni.
But Palace were a different proposition after the break and Jonny Williams missed a gilt-edged chance to put them ahead when he was sent clean through by Zaha.
The young Wales midfielder's low shot beat the dive of Seagulls goalkeeper Tomasz Kuszczak but rolled just wide of the far post.
Brighton striker Ashley Barnes twice came even closer to breaking the deadlock just a minute after climbing off the bench.
He latched onto Leonardo Ulloa's flick-on, only for Speroni to tip his shot onto the crossbar and from the resulting corner saw his header cleared off the line by Dean Moxey.
And the fine margins which decide these play-off encounters were brought home to Brighton moments later.
Palace sub Bolasie got the better of Inigo Calderon on the left and swung in a cross which Zaha, who had got in front of Wayne Bridge, met with a firm diving header which crashed into the net.
And as Brighton pushed for an equaliser they left a hole at the back which Kagisho Dikgacoi exposed by playing in Zaha, who turned Greer before thumping his shot into the roof of the net in front of the jubilant travelling fans.