It was the flawless way for Mauricio Pochettino's side to bounce back after their disappointing 3-1 defeat to Wolves at Wembley on Satudray.
Cardiff entered the contest in confident mood after four points from festive fixtures at Crystal Palace and Leicester had moved them three clear of the relegation zone.
Kane needed just over two minutes to complete his set and Spurs completed the job with goals from Christian Eriksen and Son Heung-min.
Daniel Levy played hardball, nothing new there, and Real were forced to look elsewhere, plumping for Julen Lopetegui... and look how that turned out.
Cardiff have lost their last 15 Premier League matches against the "big six" sides, conceding 47 goals across those matches, with 25 of those goals conceded coming in their six defeats this season.
While it will be relatively easy for Warnock to shrug off these losses to Champions League sides, he will hope that his players' confidence isn't affected when they are next at home, especially as they will be hosting relegation rivals Huddersfield. If Liverpool loses to City, Spurs will be back in it.
"I think they should step in now and rather than six or seven weeks, they should make it until the end of the season now and enforce it now".
"I don't care. Of course I will watch, it will be an unbelievable game and I enjoy football", he said. It was beaten 5-1 at Manchester United just before Christmas and was also thrashed 5-0 by Man City at home in September.
Neil Warnock's side made life hard for the Lilywhites on October 6 at Wembley Stadium, but Pochettino's team ground out a one-goal victory thanks to Eric Dier's early opener.
"The energy we showed from the beginning was fantastic to dominate the game".