26-year-old Kane has now scored 23 goals in 23 appearances for Tottenham and England this season.
This was the first occasion where a team managed by Mourinho came back from two goals down to win a Champions League game.
Mid-fielder Dele Alli ended a run of 16 Champions League games without a goal.
Mourinho managed his sixth club in the competition.
Kane will be crucial for Spurs in the knockout stages
Kane has been Spurs' leading man in the Champions League. After impressing over the last few seasons, he has already been doing well this term. Kane has scored five goals this season and will be a crucial force in the knockout stages.