Harry Kane had given Spurs the advantage, however, Dwight Gayle's penalty and a fine goal from his strike partner saw the new manager's homecoming in with a much-needed victory
Alan Pardew's homecoming as the Eagles' boss was met by a brave display from his new side but Spurs, on the back of a 5-3 win over Chelsea, matched Palace in the first half.
Mauricio Pochettino's men could have taken the lead when Kyle Walker's cross deflected into the path of Christian Eriksen, however he failed to make his eight-yard effort count.
Palace then had a glorious chance of its own to take the lead as Glenn Murray went one-on-one with Hugo Lloris, however the Frenchman spread himself well to deny the striker.
It took just three minutes of the second half for Spurs to take the lead, though, as Harry Kane gave Pochettino's men the advantage.
The striker, who has proven his goalscoring credentials in the first-team this season, capitalized after Nacer Chadli lost the ball, which was gleefully claimed by Kane, who arrowed his shot low past Julian Speroni.
Spurs continued to press, however. Pardew's men were effective on the counter and made the visitors pay when Benjamin Stambouli brought down Joe Ledley in the box.
It looked to be a fortuitous penalty after replays, however Dwight Gayle stepped up to peg Pochettino's men back to make it 1-1 with 20 minutes to play.
Spurs, who had looked comfortable shortly after Kane's strike, succumbed to a second Palace goal as Jason Puncheon found the bottom-right corner with a fine, sweeping shot past Lloris.
Palace continued to press through Wilfried Zaha but, more importantly, held on to seal a much-needed first win for Pardew.