Spurs had to come from behind as their newly-promoted opponents made it tough for them in north London.
Scottish midfielder John McGinn had rocked the hosts at the Tottenham Hotspur Stadium in the first half.
Click Here: toulon rugby shop melbourne
In the end, though, Kane struck a double after Spurs’ club-record signing Tanguy Ndombele had levelled for Mauricio Pochettino’s men.
The brace represented yet another first for the England captain who, having ended his August drought last year, finally scored in a Premier League opening match.
And he admitted it felt like he’d lifted a weight from his shoulders.
Kane told talkSPORT: “It’s a good start personally. It’s the first time I’ve scored in the first game in the Premier League.
“It’s nice to get that one off my back.