The England captain's fine finish in first-half stoppage time settled an even contest and moved Spurs to within five points of fourth place, albeit having played a game more than Newcastle and Manchester United.
Dan Kilpatrick was at Craven Cottage to rate the Spurs players...
Hugo Lloris 7
Got behind a number of Fulham efforts in a busy first half and made a smart late save as Fulham pushed for an equaliser.
Cristian Romero 7
Sloppy on the ball in the opening minutes but grew into the game. Booked for a high foot on Aleksandar Mitrovic.
Eric Dier 8
Relished the physical battle with Mitrovic and stood up well to the Serb.
Ben Davies 7
Steady defensively and set up Kane for a fine chance in the second half with a header across goal.
Emerson Royal 7
Tested Bernd Leno in the first half as he eyed another goal and was committed at the back.
Pierre-Emile Hojbjerg 6
Initially uncomfortable in the face of Fulham's press but more assured in the second half when Spurs had settled.
Rodrigo Bentancur 7
Composed on the ball and full of energy. Makes a huge difference to this side.
Ivan Perisic 5
Offered little in another subdued performance.
Dejan Kulusevski 7
Full of clever touches and purposeful runs.
Heung-min Son 5
Fittingly got the assist for Kane's record-equalling goal but was largely a passenger again, and lucky to avoid a red card for a studs-up challenge on Kenny Tete.
Harry Kane 8
Hauled Spurs ahead with a magnificent finish to make history and nearly secured the outright record, only for Bernd Leno to save his header.
Richarlison (Son 75') 6
Energetic but not enough time to make a real impression.
Yves Bissouna (Kulusevski 90') N/A
Not used: Forster, Doherty, Skipp, Sanchez, Sessegnon, Tanganga, Lenglet.