Kane struck in the 75th minute from close range to move beyond Andy Cole into third in the list of all-time top scorers in the competition’s history with 188 goals. It was also his 43rd effort in a Premier League London derby, which put him level with previous outright record-holder Thierry Henry.
It added to Pierre-Emile Hojbjerg’s opener for Antonio Conte’s men and while Aleksandar Mitrovic scored late on for Fulham to set up a nervy finale, Spurs held on to make it four wins and two draws from their opening six matches.
Conte had promised rotation during a busy period and five changes were made. Clement Lenglet and Richarlison were handed full debuts and the latter should have opened his account in the seventh minute but headed over Son Heung-min’s cross.
Kane had already tested Bernd Leno by this point and it was the presence of the England forward which saw Son’s cross-cum-shot ruled out for offside after 10 minutes.
Tottenham continued to push for the opener and Son had another effort deflected over after fine play by Richarlison before the South Korean fired against the crossbar in the 33rd minute following a wonderful chipped pass by Kane.
Fulham had been forced into an early substitution when Antonee Robinson limped off and his replacement Kevin Mbabu was at fault when the home side did make the breakthrough five minutes before half-time.
Mbabu was pressed impressively by Brazilian duo Richarlison and Emerson, which saw Spurs win possession close to the visitors’ penalty area and within seconds Hojbjerg had rifled into the bottom corner following a neat one-two with Richarlison.
It was just reward and Ryan Sessegnon sent another effort wide soon after but it stayed 1-0 at the break.
The opportunities kept on coming for the hosts with Eric Dier off target following more fine work from Richarlison, who himself failed to make the most of a promising opening in the 51st minute.
Marco Silva’s side provided a reminder of their quality moments later when Mitrovic got his first sight of goal and saw a deflected shot from 22 yards superbly tipped over by Hugo Lloris.
Normal service quickly resumed with Sessegnon’s low strike pushed wide by Leno and Fulham made a triple change on the hour mark with deadline-day additions Dan James and Willian introduced.
There would be no narrative goal for the visitors though with a second arriving for the home side in the 75th minute.
Sessegnon, not long after shaking off cramp, burst into the area and, despite seeing one shot blocked, was first to the loose ball and crossed in for Kane to tap home.
VAR checked whether the Tottenham forward was offside but the goal was awarded to give Kane another milestone.
Mitrovic gave Fulham a lifeline with an excellent curled effort seven minutes from time after firing into the top corner and almost forced an equaliser not long after when a deflected strike was superbly tipped over by Lloris.
It proved a vital save and despite Richarlison being denied a deserved debut goal in stoppage time, after the excellent Sessegnon was adjudged to be offside in the build-up, Tottenham held on to continue their quietly impressive start to the new season.
Spurs now turn their attention to Wednesday’s Champions League clash with Marseille while Fulham have a week to prepare for Chelsea’s visit.