Selhurst Park was rocking for the return of Pardew but the first half was a scrappy affair that saw excellent chances spurned by Christian Eriksen and Glenn Murray.
The game burst into life shortly after the break as Harry Kane continued his superb goalscoring form by firing past Julian Speroni from the edge of the box.
It looked as though the goal might be enough to secure victory for Spurs until a dramatic comeback from Palace.
Dwight Gayle levelled from the spot in the 69th minute after Benjamin Stambouli was penalised for sliding in on Joe Ledley.
And Selhurst Park erupted again 10 minutes later as Jason Puncheon drilled the winner past Hugo Lloris to send the home fans wild.
It was a dream finish for Pardew’s Palace, who for much of the match had been subdued by Spurs and restricted to few clear opportunities on goal.
With Yannick Bolasie and Mile Jedinak away on international duty, Pardew handed a first Premier League start of the season to Murray alongside Gayle up front.
Spurs made two changes from their New Year’s Day win over Chelsea, bringing in Mousa Dembele and Benjamin Stambouli for Ryan Mason and Nabil Bentaleb, and they dominated possession in the early stages.
When Palace did manage to string together a decent spell of passes each was loudly cheered by the home fans, but it should have been Spurs who were celebrating after 22 minutes.
Kyle Walker’s low cross from the right bounced up for Eriksen, who got a good contact but fired wide from eight yards out.
Palace had their first chance moments later as James McArthur headed over from Gayle’s cross, and the home side started to show signs of improvement.
They should have taken the lead after 34 minutes when McArthur flicked the ball on for Murray, who was one-on-one with Lloris but saw his shot well saved by the keeper.
That was to be the best opening of a scrappy first half but the game burst into life shortly after the break as Kane broke the deadlock.
There looked to be little on when the ball fell for the striker on the edge of the box but he got the ball out of feet and fired a fine shot into the bottom corner.
For the next 15 minutes it looked as though the goal might be decisive as Spurs looked comfortable in possession and Palace struggled to muster a reply.
But Stambouli’s decision to slide in on Ledley in the box in the 67th minute proved to be pivotal.
Referee Anthony Taylor pointed to the spot and Gayle dispatched the penalty past Lloris to level the scores.
The momentum now looked to be with Palace and, moments after Puncheon was incensed by a decision not to award the hosts a handball, the winger fired home the winner.
Substitute Wilfried Zaha showed excellent skill on the left to beat two defenders and his cross deflected into the path of Puncheon, who swept his shot into the corner.
The goal sent Selhurst Park into raptures and the home side held on to secure victory despite a late Spurs penalty appeal after a challenge in the box on Kane by Ledley.
Crystal Palace: Speroni (6), Ward (6), Dann (6), Delaney (6), Kelly (6), Ledley (6), Puncheon (8), McArthur (6), Bannan (5), Gayle (7), Murray (5).
Subs: Guedioura (5), Campbell (5), Zaha (6).
Tottenham Hotspur: Lloris (6), Walker (6), Fazio (5), Vertonghen (6), Rose (5), Stambouli (5), Dembele (6), Townsend (5), Eriksen (6), Chaldi (6), Kane (7).
Subs: Soldado (5), Capoue (6).
Man of the match: Jason Puncheon.