In-form striker Harry Kane opened the scoring after 49 minutes, Tottenham at that stage appearing well placed to build on their superb 5-3 triumph over Chelsea on New Year's Day.
But this London derby did not have such a happy ending for Mauricio Pochettino's team, as Dwight Gayle netted a 69th-minute penalty after Benjamin Stambouli had rashly fouled Joe Ledley.
Pardew introduced Wilfried Zaha shortly afterwards – the forward giving the Tottenham defence and Kyle Walker in particular a torrid time before creating the winner for Jason Puncheon.
A fervent Selhurst Park crowd was forced to endure six minutes of stoppage time before celebrating a result that lifts their team out of the relegation zone.
Pardew was without Yannick Bolasie and Mile Jedinak, away on Africa Cup of Nations duty with DR Congo and at the Asian Cup with Australia respectively, while he handed Glenn Murray a maiden Premier League start of the season in attack.
Midfielders Mousa Dembele and Stambouli continued in place of Ryan Mason and Nabil Bentaleb for Tottenham, who controlled much of the opening half.
They were met by a disciplined Palace defence, while visiting winger Nacer Chadli received neither a penalty nor a yellow card for a theatrical 13th-minute tumble in the area.
Kane scuffed a low shot into the arms of Palace goalkeeper Julian Speroni before Christian Eriksen spurned a glorious chance to open the scoring after 22 minutes.
A nicely worked Tottenham move gave Walker room to cross from the right and, although his low delivery was just behind the midfielder, Eriksen should have done better than thumping a shot wide from six yards.
Murray was largely feeding off scraps up front for Palace but he was presented with a clear opening 10 minutes before half-time – the on-rushing Hugo Lloris diverting his shot behind after James McArthur's prodded throughball.
Lloris did not distinguish himself in the same fashion early in the second half, missing a punch from a corner before Gayle lost his footing and the chance was lost.
Tottenham's nerves were settled in the 49th minute by the familiar sight of Kane drilling the ball clinically into the net for an 18th time this term.
There were suspicions of offside when the ball broke to the England Under-21 forward from Chadli’s forward run, but Kane displayed fine close control and sent a superb finish across Speroni.
Gayle poked a set-piece goalwards from close-range but sharp reactions by Lloris denied Palace an almost instant response.
But Stambouli's inexplicable challenge on Ledley gave Gayle another chance to get the better of Lloris from the spot, and he did so with aplomb.
Palace felt they should have been awarded a second spot-kick when a cross struck Walker's arm, but Pardew was able to forget his loud protests when Puncheon lashed a shot home 10 minutes from time to leave the hosts a point clear of the bottom three.
