The England international opened the scoring for Spurs against Everton at White Hart Lane with his superb strike from 20 yards in the 20th minute.
He then gave Spurs a two-goal advantage shortly after the break when he side-footed past Joel Robles at his near post in the 56th minute.
Everton striker Lukaku handed the Toffees hope with his composed effort nine minutes from time but, despite his goal, Kane leads the Premier League goalscoring charts with 19 strikes and four assists.
Lukaku is one behind with 18 goals and four assists while Arsenal forward Sanchez has 17 goals and nine assists following Arsene Wenger's decision to start the Chile star on the bench for Arsenal's crunch game with Liverpool on Saturday, which the Gunners lost 3-1.
Chelsea striker Diego Costa - who is expected to start against West Ham on Monday night - sits on 16 goals and five assists for the season so far, one ahead of Manchester United's Zlatan Ibrahimovic who has 15 goals and four assists.