The forward, on his way to Old Trafford in the summer, notched both goals to down Gus Poyet's men and book a date at Wembley to challenge Watford for a place in the Premier League
The young forward headed in from a fine Yannick Bolasie cross shortly after the midway point in the second half before thumping home a second in the later stages to send the Eagles to the new Wembley for the first time at the expense of their fierce rivals.
With no fresh injury concerns with which to contend, Gus Poyet opted to field the same side that secured a goalless draw in the first leg but his Palace counterpart Ian Holloway was not so lucky. The visitors were without top scorer Glenn Murray after he suffered a nasty knee injury during Friday's stalemate; he was replaced by Aaron Wilbraham in Palace's only change.
The first half continued where Friday's tense affair left off but it was the visitors who started brighter as Owen Garvan's driven cross was flicked goalwards by Wilbraham, though his effort went well wide.
At the other end, Zaha surrendered possession cheaply on the edge of the Palace area but Julian Speroni bailed his teammate out with a smart save from Will Buckley's well-struck shot.
Spurred on by the passionate home fans, Brighton began to dominate proceedings as David Lopez and then Matthew Upson went close to breaking the deadlock but Holloway's side held firm.
As the half developed, Zaha saw more of the ball and it was his low cross which caused a moment of uncertainty in the Brighton rearguard before Upson cleared the danger from under his crossbar.
And it was the Manchester United-bound attacker who provided Jon Williams with a glorious opportunity to draw first blood but, with only Tomasz Kuszczak to beat, the Wales international fired narrowly wide.
It was the wake-up call that the hosts needed as the tie came to life for the first time. Poyet responded by introducing Ashley Barnes and the substitution almost paid immediate dividends.
However, Speroni pulled off a superb save to tip Barnes's first-time effort onto the crossbar and, from the resulting corner, Dean Moxey hacked the substitute’s header off the line.
Having soaked up the pressure, Palace went down the other end and landed the killer blow. Bolasie's inswinging cross from the left was met perfectly by Zaha, who escaped the attention of Wayne Bridge to head home and send the away fans into raptures.
Despite the introduction of Kazenga LuaLua and the desperate support of a packed Amex Stadium, the Seagulls could not find the cutting edge for a late rally.
Instead, it was Zaha who had the final say as he turned away from Gordon Greer before smashing in a left-footed shot via the under side of the crossbar to secure Palace's place in the final and a chance to end their eight year absence from the top flight.