The Lilywhites were heading for a second straight home defeat thanks to an exquisite Eberechi Eze free kick, but Timo Werner, Cristian Romero and Son Heung-min found the mark to hand Oliver Glasner his first defeat in the Eagles dugout.
With Richarlison beginning a three-week absence due to a knee injury, Werner was drafted back into the Tottenham XI, while Eze made his long-awaited return to the Palace side for the first time since January.
Boosted by the playmaker's comeback and with the wind in their sails after last weekend's dominant beating of Burnley, Glasner's men went toe-to-toe with Spurs in the early minutes, but neither goalkeeper was truly tested.
That was until the 18th minute, when the recalled Werner was presented with a one-on-one against Sam Johnstone after being fed by Son and tried to skip past the Englishman, but the Palace number one came up trumps and gathered the ball at the German's feet.
Spurs customarily dominated the ball as the first half progressed, but Palace's deep block was stifling the Lilywhites' threat and preventing the hosts from breaking the lines or finding runners out wide.
Ange Postecoglou's men were fizzing the ball about with more purpose at the start of the second period, and captain Son came agonisingly close to breaking the deadlock in the 54th minute, but he struck the woodwork when attempting to beat Johnstone at his near post.
However, Spurs' brief period of improvement would count for nought in the 59th minute, as after being barged over by Rodrigo Bentancur in a promising free-kick position, Eze lined up his set piece 20 yards from goal and blasted a venomous strike past Guglielmo Vicario to give the Eagles the lead.
Rather than opting for an up and over-the-wall attempt, Eze found a gap between Vicario and his near post, and the Italian - who had taken a slight step to his right - could not react quickly enough to keep out the Englishman's terrific strike.
Tottenham belatedly forced Johnstone into action after falling behind - Werner's top-corner-bound attempt was palmed away by the Palace keeper in the 62nd minute - three moments before Brennan Johnson blazed over with a close-range chance that looked more difficult to miss.
The Welshman more than made amends in the 77th minute, though, robbing Joachim Andersen of the ball and evading Jefferson Lerma before squaring for Werner, who also atoned for his first-half error with a clinical side-footed finish to level the score.
The hosts' equaliser was deserved, and akin to their 2-1 beating of Brighton & Hove Albion three weeks ago, Postecoglou's men completed another second-half turnaround just three minutes after Werner struck.
Found by a clever throw-in from Emerson Royal, James Maddison lifted a volleyed pass over the top of Palace heads from the right-hand side of the box, and Romero beat Joel Ward in the air to direct a deft header into the bottom corner.
The result of Saturday's London derby was put beyond any reasonable doubt with 88 minutes on the clock, as a desperate Palace were caught out at the back and Johnson released Son, who ruthlessly finished into the far corner as Johnstone dived the other way.
Thanks to their latest home turnaround, Postecoglou's men remain fifth in the rankings but have temporarily reduced the gap to Aston Villa to two points, and there is no change to Palace's 13th-placed standing.
Tottenham hit the road again next Sunday to pit their wits against Aston Villa, one day before Glasner's side host Luton Town at Selhurst Park.