Spurs had laboured in their previous home matches this season, having to come from behind to beat newly promoted Aston Villa and then falling to a 1-0 defeat against Newcastle.
Tottenham fans may have feared another frustrating afternoon against London rivals Palace.
Roy Hodgson's side arrived lying fourth in the league table and boasting the best defensive record, having conceded just two goals in their opening four matches.
The Eagles have also developed a reputation for winning away against top-six sides, having triumphed at all of those elite teams apart from Spurs since the start of the 2016/17 season.
But Mauricio Pochettino's side blew their visitors away with four first-half strikes, Son Heung-min scoring either side of a Patrick van Aanholt own goal before Erik Lamela got in on the act in a victory that took the north Londoners up to third in the table.
Pochettino made just one change to the side that had drawn 2-2 with Arsenal before the international break, selecting Serge Aurier at right-back in a 4-2-3-1 formation.
It was Aurier's first league start since February 23, and the Ivorian would probably have been overlooked once again if Juan Foyth or Kyle Walker-Peters had been available.
In the very first minute, Son found himself in space inside the box and sent a low shot at goalkeeper Vicente Guaita.
Toby Alderweireld then dissected Palace's centre-backs with a ball over the top to Harry Kane, who was also unable to beat Guaita.
The visitors should therefore have spotted the danger when Alderweireld sent another long pass up towards Son but Mamadou Sakho got caught underneath the ball, allowing Son to bring it down, cut inside and find the bottom right corner.
Eleven minutes later Aurier fired in a low cross that deflected in off Van Aanholt at the near post, and two minutes after that the right-back hung up a cross to the far post, where Son arrived unmarked and volleyed home six yards out.
It was the South Korean's fifth goal in his four home league matches against Palace, and he was involved in the move for the final goal before the break, passing wide to Kane, whose low cross was finished by Lamela.
Son nearly completed his hat-trick after half-time when he burst past Sakho and lobbed Guaita from a tight angle, only to find the near side netting, while a powerful Aurier shot was blocked.
Pochettino said at the start of this month that when the European transfer window closed, ending speculation about the immediate futures of some of his players, he would "make a big party and celebrate".
Content his side were safe, the Argentine's thoughts turned to Wednesday's Champions League match against Olympiakos and he withdrew Harry Winks, Danny Rose and Kane.
Palace, having suffered a ninth straight league defeat to Spurs, will wonder how long it will be before they are next in the top four again. (AFP)