Kane got his side up and running in their quarter-final tie with a fine finish inside four minutes at the Stadio Olimpico, England's earliest goal in a Euros match since 2004.
Harry Maguire's bullet header less than a minute into the second half made it two, before captain Kane nodded home his second of the game and third of the tournament four minutes later.
Substitute Jordan Henderson completed the rout with his first international goal to ensure England's comfortable passage into the last four, where they face the Danes at Wembley on Wednesday for a place in the final at the same stadium.
Here’s how James Robson rated those on show...
Smart save from Yaremchuk after Ukraine rallied in the first half. His outstanding tournament continues.
Kyle Walker 7
Caught out to allow Yaremchuk and a couple of shaky moments. But found his composure more as the game went on.
John Stones 8
Some important interceptions early on. Very controlled throughout. That partnership with Maguire gets better and better.
Harry Maguire 8
Very assured. Got his positioning spot on throughout and came up with a towering header to double England’s lead.
Luke Shaw 9
Very positive going forward with good delivery from set-pieces and also set up Sancho for a first half effort that might have extended England’s lead. After Jose Mourinho’s criticism, he delivered the perfect response – setting up Maguire and then another cross for Kane’s second.
Kalvin Phillips 7
Helped England control midfield – particularly early on, but had to adjust when Ukraine switched to four at the back and got more of the ball.
Declan Rice 7
Fierce effort almost added to England’s lead. Totally assured and he’ll be fine for the semi after being substituted in the second half.
Mason Mount 8
Full of energy and invention on his return to the team. Has surely done enough to keep his place – including the delivery for Henderson’s goal.
Jadon Sancho 8
Very bright after finally being given the chance from the start. The new Manchester United signing’s feet were too fast for Ukraine’s defenders, who left standing.
Harry Kane 9
Was there ever any doubt? Broke his duck against Germany and here he was doing what he does best – putting the ball in the back of the net. Got two – could’ve had more.
Raheem Sterling 8
England’s player of the tournament by a mile made things happen again. Brilliant run and pass for Kane’s opener. A constant threat.
Jordan Henderson (Rice, 57) 7
Came off the bench and found the back of the net for his first England goal.
Jude Bellingham (Phillips, 65) 6
So assured every time he plays.
Marcus Rashford (Sterling, 65) 5
Would have loved to have got on the score sheet, but England’s fluidity went with so many changes.
Kieran Trippier (Shaw, 65) 5
Came on and helped England keep their shape at the back.
Dominic Calvert-Lewin (Kane, 73) 5
Valuable minutes for him, but no chances.
Subs: Grealish, Johnstone, Foden, Mings, Chilwell, Ramsdale, Coady,