Spurs now take a significant advantage ahead of their trip to Croatia next week.
But Kane and Son Heung-min started against Zagreb, and it was the former who opened the scoring with a rebound after 25 minutes.
The England captain made it two with a low finish in the 70th minute before limping off with a knock to his knee.
Spurs will now travel to local rivals Arsenal for Sunday's North London derby.
On his side's win over Dinamo, Mourinho said: "I believe one more goal would be a good reflection of the game and would put us in a much better position. But before the game if you asked if 2-0 was a good result I would say. It is only a good result if we do the job there.
"It will be a difficult match. At home they will feel more comfortable to have a go with nothing to lose."
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