Teddy Sheringham had previously held the record of 97 goals in England’s top flight for the club, but Kane met and surpassed the tally with his double, tapping home early in the second half (47) before bobbling the record-breaking goal into the net 12 minutes later.
Heung-Min Son (26) had opened the scoring in the first half, and matched his own Tottenham record as he netted in his fifth consecutive home Premier League game – equalling Jermain Defoe’s previous efforts – and Christian Eriksen rounded off proceedings late on (81), sweeping home a fine team move.
Tottenham remain in fifth spot, level on 44 points and goal difference with Liverpool ahead of their game with Manchester City live on Sky Sports on Sunday, while Everton are also still in ninth place.
Spurs saw the better of the ball in the opening period and could have taken the lead in the 15th minute. Eriksen whipped a superb free-kick into the box, which met the head of Son at the near post after a bursting run, but he could only flash the effort over the crossbar.
Everton had the ball in the net eight minutes later, but it was ruled out for offside. Gylfi Sigurdsson’s corner was flicked on by debutant Cenk Tosun, finding the head of Wayne Rooney, and although his glancing effort beat Hugo Lloris, the linesman already had his flag raised.
This seemed to put the fire into Tottenham as Son scored the opening not long after. A great switch of flanks from Eriksen saw him pick out Serge Aurier on the right hand side, who in turn fizzed an inviting ball into the box. Son was there waiting to tap home, and continue his fine run of form in front of goal.
The South Korea international was involved again as Kane netted his first of the game two minutes after the restart. He took the ball around Jonjoe Kenny before bursting down the left-hand side, with his cross into the box tapped home by a waiting Kane as he equalled Sheringham’s record.
Son could have added the third in the 58th minute, collecting a cross-field pass from Kane before cutting across the top of the box and striking, but his thunderous effort thrashed against the woodwork before going wide, although Kane made sure to net another Spurs goal a minute later.
Eric Dier curled the ball into the area and Kane was again waiting to tap home, with the effort ricocheting off his foot and shin before bobbling past Jordan Pickford as he took his Premier League goals tally for Tottenham to 98 and became their leading goalscorer in the competition – and counting.
But perhaps the best goal of the evening came in the 81st minute after a fine flowing move saw Eriksen net Spurs’ fourth. Five players were involved in the build-up, but it was a superb back heel from Alli at the edge of the box that found Eriksen on the left, before he powered home to seal a superb Spurs victory.