The Barcelona superstar bagged a superb double and pulled the strings as Philippe Coutinho and Ivan Rakitic also netted.
Kane, who this week said his ambition was to score more career goals than Messi, notched for Spurs along with Erik Lamela.
Messi even hit the post twice at Wembley.
BT pundit Rio Ferdinand said: “You have to marvel at this guy. I feel blessed I was in this stadium live to watch him.
“I will tell my kids about it tomorrow on the school run.
“This guy, what he does on the football pitch, is just ridiculous.
“It’s like he’s got a remote control in his hand, he assesses the situation and says ‘Yeah, let me just plot in the location and I’ll put the ball exactly where I want’.
“His weight of pass and his decision-making is unrivalled — and when he gets in to finish he is as cool as you like.
“Messi has been stupendous.”
Spurs keeper Hugo Lloris came haring off his line after 92 seconds, leaving ex-Liverpool ace Coutinho free to tuck home.
Rakitic added a volley before Messi capped off his dazzling display with two goals.
Ferdinand added: “Lloris, what he’s doing out there I don’t know? I would love to know what he says in the dressing room.
“He’s shaking his head, that’s a big mistake.”
Former Barca striker Henrik Larsson added: “Lloris has gone out to no-man’s land.
“The game has just started, and your game plan as a manager is out of the window.”
Lloris again inexplicably came racing off his line with the score at 3-2 — but was bailed out by a Toby Alderweireld tackle.
Ex-England defender Ferdinand also raved about Rakitic’s goal.
He added: “He’s got both feet off the floor, it’s a full hit, venom — it’s beautiful to watch in slow motion.
“He’ll have a picture of that on his wall in his house in the future.”
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