It was Tottenham's first win in eight matches in all competitions and moved them to seventh with 45 points -- one behind Manchester United in fifth spot.
"First of all three points were not important, they were crucial," Mourinho told reporters. "I said to the players 'don't think if we don't win this match we can still think about chances', it was three points or nothing.
"We were too slow and predictable in the first half but we were stronger and more intense in the second half."
With seven games remaining, Tottenham have at least given themselves a chance of ending what has been a disappointing season with a flourish -- helped by the fact Mourinho now has a full squad to choose from with Kane, Son Heung-min and Moussa Sissoko all fit again after long injury lay-offs.
Kane, who recovered from a hamstring tendon injury during the three-month shutdown, said he was delighted to get back on the scoresheet in his second game back.
"When you've been out for over six months it's about getting that feeling back on the pitch," the England skipper said.
"I'm in good shape. I've been working very hard. I feel as good as I've ever done."
Sky Sports analyst Paul Merson said after Spurs' 1-1 draw with Manchester United last Friday that Kane would struggle to score goals in Mourinho's conservative system and that the striker would consider switching clubs if he continued with his approach. After Tuesday match, Kane addressed those concerns with the BBC.
"I've got no problem with how the manager plays. He's here to win, we're here to win games... obviously this season, to get into the Champions League and next season to progress and try to win something," he said.
"People, pundits have their opinions."
Teammate Eric Dier said the long pause to the season may have helped Tottenham.
"It's a strange feeling because before lockdown we weren't in good form but we have been working very hard. We have felt positive in the restart and hopefully that continues.
"Champions League is the aim. We knew if we didn't win tonight it might be too far."