Cardiff's poor record against the top teams continued, losing their last 15 Premier League matches against the "big six" sides, conceding 45 goals.
After Kane launched an attack, surging from deep, Kieran Trippier crossed and the England forward had a simple tap-in when the ball ricocheted off Cardiff defender Sean Morrison.
It was Kane's 14th league goal, moving him alongside Arsenal striker Pierre-Emerick Aubameyang atop the scoring list and one above current Golden Boot holder Mohamed Salah, the Liverpool forward.
Spurs made it 2-0 after just 12 minutes with a classy goal from Eriksen.
"I'm very pleased, the one thing I need to say is we suffered without rest between the games and therefore from the players it was magnificent", said the 46-year-old Argentinian.
Spurs bounced back from Saturday's shock home defeat to Wolves with a 3-0 win that saw Harry Kane, Christian Eriksen and Son Heung-min score inside the opening 26 minutes. "Of course I will watch it, it will be an unbelievable game and I enjoy football".
EPL: Kane keeps Tottenham in title hunt with Cardiff romp
On making changes, Pochettino added: "It is more collective than two, three or four players".
Cardiff found it hard to get possession after that, although substitute Junior Hoilett did enliven them after the interval in their search for a first goal against Spurs for 41 years. It was beaten 5-1 at Manchester United just before Christmas and was also thrashed 5-0 by Man City at home in September.
"All the planning goes out of the window".
Daniel Levy played hardball, nothing new there, and Real were forced to look elsewhere, plumping for Julen Lopetegui... and look how that turned out.
For all of the eagerness of the media department to move on the discussion, the fact that "Poch" didn't come straight out and flatly deny he wanted the Manchester United manager's job as soon as his candidacy was mentioned meant that the floundering officer was left batting away questions like his life depended on it.
"From the beginning today we showed massive energy and I think that is the team we want, and expect, to see to get a good performance on the pitch".