Kane's double, added to by countryman Dele Alli and Son Heung-min, handed Spurs an emphatic victory that fired them up to third in the Premier League.
They are now level on points with Manchester United and have firmly established themselves as title contenders.
Manchester City still lead the way on 25 points, but Tottenham look like the only team that can stop the Citizens at the moment.
Defensively Spurs were a bit shaky at times - Mohamed Salah's goal should never have happened - but going forward they were nothing short of phenomenal.
Kane, Alli, Son and Christian Eriksen were fantastic and caused Liverpool's awful defence all kinds of problems throughout the 90 minutes.
And Kane believes they could - and should - have scored more. He said in a post-match interview with Son: "It (the win) was unbelievable.
"When we went 2-1 we had to stay focused and then we played well in the second half to see it out. We could have scored more. We played really well and defensively we were solid.
"We played well on the counter attack. "Trips (Kieran Trippier) put a lovely ball over the top. I finished it and was happy to see it go in. [The] second bounced nicely for me.
"We are in very good form. Tough month but started it well. There is plenty of time to go and we need to keep on going."
Kane was once again the star of the show with his brace, but his England teammate, Alli, was just as good.
His goal in the 45th minute was a smashing volley that gave Simon Mignolet no chance and he spent the entire second half just embarrassing Liverpool's players.
Emre Can was the victim of one nutmeg, as was James Milner, but Alli's finest piece of skill came in the 53rd minute.
In the video below, Alli is backed into a corner by Salah and Milner but escapes their clutches with a naughty back-heeled pass straight to Kane. Check it out.
ALLI MUGS OFF SALAH AND MILNER
Now that's what you call confidence. There are rumours Alli wants £160,000-per-week wages when he signs a new contract at Tottenham and they'd be fools to not give him it.
Alli is still only 21-years-old and if he continues improving at this rate, he'll be genuinely world class within the next few years.