Wickham's towering header just after the hour mark secured a 2-1 win over Watford and a return to Wembley to face Manchester United next month.
Yannick Bolasie nodded Palace into a ninth-minute lead but Troy Deeney hauled the Hornets level just after half-time.
However, Wickham's strike means Pardew has the chance to make it third time lucky, having lost in the final as a player to United in 1990 and as manager of West Ham against Liverpool in 2006
Pardew, of course, had memorably nodded the Eagles into the final with their dramatic extra-time winner against Liverpool
And 26 years later he was celebrating with a clenched fist and a knowing grin as his current side created a carbon copy for Bolasie's opener
This time it was Yohan Cabaye, rather than Andy Gray, who swung in a corner towards the near post.
Damien Delaney reprised the Andy Thorn flick-on and Bolasie applied the Pardew finish, squeezing his header between the far post and Hornets goalkeeper Costel Pantilimon.
Watford attempted to hit back but were limited to Deeney's curler over the crossbar and Allan Nyom's deep cross, which caused momentary concern in the Palace area before Joel Ward turned the ball behind
The Hornets suffered a major blow after half an hour when midfielder Etienne Capoue, an influential figure all season, collapsed in agony after a seemingly innocuous off-the-ball collision with Bolasie.
The France international departed on a stretcher with a knee injury and with him went any Watford momentum for the remainder of the first half.
Indeed, they could count themselves fortunate not to be two down at the interval after Wilfried Zaha's cross clearly hit the hand of Nathan Ake in the area - but referee Craig Pawson waved away Palace's appeals for a penalty.
After the break Bolasie twisted and turned his way into the Watford box and forced Pantilimon to saved a fierce angled drive with his feet.
A Hornets revival still appeared unlikely, until they forced a corner following Ben Watson's deflected free-kick 10 minutes into the second half.
Jose Jurado's delivery was perfect for Deeney, who got in front of his marker Scott Dann to plant a firm header past Wayne Hennessey.
However, Watford were level for just six minutes before Pape Souare sent an inviting high cross towards Wickham, who rose above Ake and guided a towering header across Pantilimon and into the far corner.
Again Watford tried to muster a response but Odion Ighalo, a peripheral figure all afternoon, blazed over the crossbar and sub Adlene Guedioura fired wide in stoppage time.
So the Hornets' cup run came to an end while Pardew, who has long felt this competition may just owe him one, gets another tilt at United and glory for Palace.
TWEET OF THE MATCH
Nigel Martyn @nmartyn25 "Get in @CPFC great result !! Hope @CEO4TAG gets thrown in the bath with his suit on like Ron Noades did 26 years ago"
PLAYER RATINGS
Crystal Palace
Wayne Hennessey: 6
Joel Ward: 7
Scott Dann: 6
Damien Delaney: 7
Pape Souare: 7
Mile Jedinak: 7
Yohan Cabaye: 7
Wilfried Zaha: 7
Jason Puncheon: 5
Yannick Bolasie: 8
Connor Wickham: 8
Subs
James McArthur: 6
Bakary Sako: 5
Emmanuel Adebayor: 5
Watford
Costel Pantilimon: 5
Allan Nyom: 6
Miguel Britos: 6
Craig Cathcart: 6
Nathan Ake: 7
Almen Abdi: 5
Ben Watson: 6
Etienne Capoue: 5
Jose Manuel Jurado: 6
Troy Deeney: 7
Odion Ighalo: 6
Subs
Mario Suarez: 6
Adlene Guedioura: 6
Ikechi Anya: 5
STAR MAN
Yannick Bolasie
Headed Crystal Palace's opening goal and provided their most consistent attacking threat to stretch Watford's defence and prevent them from building attacks of their own
Demonstrated unexpected leadership in doing so, too.
MOMENT OF THE MATCH
Odion Ighalo, so impressive during the first half of the season, was through on goal, with time, space, and the ball falling nicely to him when Watford desperately needed an equalising goal
Despite being the finest finisher on the pitch, he shot harmlessly over the bar
On such moments are games decided.
VIEW FROM THE BENCH
Alan Pardew unexpectedly selected Connor Wickham over Emmanuel Adebayor and was rewarded when the promising striker headed Palace's winning goal
His inclusion of Mile Jedinak also allowed Yohan Cabaye, Wilfried Zaha and Bolasie to impress as they did
Quique Sanchez Flores' Watford were too often narrow and stretched, even though the Spaniard oversaw an improvement in the second half
It was not his fault Ighalo's finishing disappointed.
MOAN OF THE MATCH
There is little question that more questions will be asked of Watford manager Quique Sanchez Flores, given defeat effectively ended their season
Any criticism of him is entirely unjustified, though: he appears a better manager than Watford deserve and has overseen an impressive first season in English football, regardless of their defeat
They should be offering him a new contract and encouraging him to build.
WHO'S UP NEXT?
Newcastle v Crystal Palace, Barclays Premier League (Saturday, April 30)
Watford v Aston Villa, Barclays Premier League (Saturday, April 30)
Source : PA
Source: PA