Loan star Bale had netted just four times in his first 16 games back at Spurs, but his double on Sunday took his tally to six across his subsequent six appearances.
Kane assisted both goals, either side of a Christian Benteke header that only briefly pegged Jose Mourinho's men back, before the England captain added a sensational third and then the fourth for a double of his own.
Son Heung-min laid on the striker's second for the pair's 14th goal combination of the campaign, a new Premier League record, as a third straight victory took Tottenham into the top six.
The star of the show from the outset, Bale had already crafted a clear opening for Son Heung-min, nodded wastefully straight at Vicente Guaita, when he netted the opener after 25 minutes.
Lucas Moura led the Spurs press and pinched the ball from Luka Milivojevic before feeding Kane, who drilled in a low centre that found Bale with an open goal and a simple finish.
Unfortunately for Tottenham, Benteke was clinical from Palace's very first attempt on the stroke of half-time as he directed Milivojevic's left-wing cross into the top-right corner with a thumping header.
But Bale picked out the same corner at the same end four minutes after the restart, climbing highest when Kane nodded Sergio Reguilon's delivery back across goal.
Following two assists, Kane then supplied the pick of the goals, a first-time effort from 20 yards that flew over Guaita's head just 138 seconds after he had last been beaten.
Wilfried Zaha, returning from injury as a half-time substitute, was unfortunate to strike the post with a left-footed shot, but Palace were soon picked apart again as a gorgeous Erik Lamela pass teed up Son's volleyed cross onto the waiting head of Kane.