Kane netted a header just after half-time to give Spurs a deserved success although their wastefulness in front of goal almost came back to haunt them in stoppage time.
The first chance arrived when Spurs went on a typically swift counter-attack down the left. Dele Alli’s centre was there to be converted for Kane but a combination of Shkodran Mustafi and Petr Cech denied him.
At the other end, Jack Wilshere’s threaded pass sent Pierre-Emerick Aubameyang scampering towards the Tottenham goal but the offside flag marginally got the better of him.
Christian Eriksen almost teed up Kane midway through the opening half but his cross just out of reach and the forward could only head over the bar.
As the break approached, Mesut Ozil’s cross gave Nacho Monreal a chance to continue his recent goal-burst but he was denied by Hugo Lloris.
Spurs didn’t have to wait long for their breakthrough goal after the break. Ben Davies’ teasing cross from the left was perfect for Kane, who outmuscled Mustafi before landing a downward header back across the goal and into the bottom corner.
With his 101st goal claimed, Kane almost doubled his tally but a powerful shot from 20 yards was beaten away by Cech.
Arsene Wenger sent for Alex Iwobi and Alexandre Lacazette from the bench midway through the second half, with Henrikh Mkhitarayan and Mohamed Elneny hauled off.
Wilshere curled a shot from the edge of the box at the midpoint of the half that had Lloris fully extended to keep it out.
With 20 minutes to play, Alli had a chance to give Tottenham daylight when sent one-on-one with Cech but his half-hearted toe-poke went around the Arsenal goalkeeper and also his upright.
Kieran Tripper went close again as Spurs passed up a number of chances to make the game safe. It almost came back to bite them during injury time, with Iwobi’s passing finding Lacazette.
The Frenchman darted between two Spurs defenders and beat Lloris, only to drag his shot wide of the far post, much to Wenger’s frustration.
With the final act, Ozil smashed a free-kick into a defensive wall, leaving Spurs to take the spoils.
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.