The duo combined twice with Kane the architect for both goals by the Real Madrid loanee before the England captain hit a wonder strike and then created history with another in the 76th minute.
Son Heung-min assisted Kane's second and it was their 14th goal combination in the Premier League this season to beat the previous record of 13 set by Alan Shearer and Chris Sutton for Blackburn back in the 1994-95 season.
Christian Benteke had threatened to spoil proceedings for Jose Mourinho's side when he equalised just before half-time, but two quickfire goals after the break ensured Spurs were able to secure a fifth straight victory.
Dele Alli was back on the bench after his second league start of the season at Fulham in midweek while the visitors listed the returning Wilfried Zaha as a substitute.
Bale showed no early ill-effects on his third consecutive start and should have had an assist in the sixth minute but Son headed straight at Palace goalkeeper Vicente Guaita.
The Welsh attacker had slalomed between two opponents to create the chance and it was a sign of things to come.
After a brace in Tottenham's win over Burnley last weekend, Bale added to his tally again with 25 minutes on the clock.
Palace captain Luka Milivojevic was dispossessed by Lucas Moura deep inside his own half and Kane dropped a shoulder to beat the midfielder and race into the area where he squared for Bale to tap in.
It was a poor way for the visitors to concede and not long after the hosts almost produced a superb team move but Sergio Reguilon sliced wide on the volley.
A flurry of corners in quick succession saw Palace build some momentum and in the first minute of stoppage time they levelled against the run of play.
Ebere Eze found Milivojevic in space and the captain atoned for his earlier error with a fine delivery into the area where Benteke headed home for his fifth goal of the season.
Zaha was introduced at the break, but he was largely a spectator during a lightning-quick start to the second period where Tottenham scored twice in the space of three minutes.
First Bale doubled his tally for the night when he nodded home from Kane's header across the face of goal after another excellent Reguilon cross in the 49th minute.
It made it 10 goals for the season for the Spurs number nine and back-to-back braces at home, but soon the focus was on the creator.
A slick move was concluded in style when Matt Doherty cut back for Kane in space and he produced a 25-yard curler into the top corner to leave Guaita with no chance.
The Bale and Kane show was ended in the 70th minute when the Real Madrid loanee was replaced but it had been another impressive showing to continue his return to form.
A minute before the substitution Zaha had almost reduced the deficit but his shot from outside the area hit the post.
There was still time for one more Spurs goal and it proved a record-breaking effort when Son squared for Kane to head in from close range for their 14th goal combination in the Premier League this season.
It bettered Shearer and Sutton's efforts of 13 for Blackburn 26 years ago and ensured the 4-1 win for Tottenham moved them up to sixth in the table while Palace remain in 13th.