Kane ended his international scoring drought by netting in the 2-0 last-16 defeat of Germany in midweek and he put England ahead inside four minutes of this quarter-final on a sweaty evening in the Italian capital.
Gareth Southgate’s side then put the tie out of sight with two more goals early in the second half, one from Harry Maguire before Kane netted again.
Substitute Jordan Henderson got the fourth, and as Denmark lie in wait at Wembley on Wednesday England will be confident of going on to reach a first-ever European Championship final and even now claiming a first major international title since 1966.
“We are on the right track for sure, but we haven’t done anything yet. We have got a massive semi-final to look forward to now at Wembley. What an occasion, what a moment to be involved in,” Kane said.
The draw here was kind for them, with Ukraine surely as weak an opponent as they could hope to face in a quarter-final, a stage at which they have lost to the likes of Italy and Portugal in recent European Championships.
However, the statistics are impressive, with England having come through five games at this tournament all without conceding a goal.
Some of their play in wide areas was outstanding, with Raheem Sterling and Jadon Sancho too hot for Ukraine to handle.
Kane, their captain, had gone close to eight hours without finding the net for his country but his opener here was his second in just eight minutes following the late strike that secured victory over Germany.
“It was a fantastic performance from everyone really, the perfect night for us,” Kane added.
Their display at the Stadio Olimpico was a step-up in class in the final third to previous games at the Euro and they will be favourites at home against a Danish side who played their own quarter-final against the Czech Republic on Saturday in distant Baku.
– Hat-trick of headers –
This will be the only match England play away from home in the competition and, with Italy currently imposing a five-day quarantine on arrivals from the United Kingdom, the number of England fans in Rome was limited.
However, they still made themselves heard in the crowd of under 12,000.
They had plenty to celebrate, unlike their Ukrainian counterparts, as Andriy Shevchenko’s team came up short in their bid to take the country to a first major tournament semi-final.
“We can be proud. Obviously, we didn’t get the result we wanted but we are on the right track,” insisted Shevchenko, who said England had been “pragmatic”.
Ukraine’s chances of shocking England looked dead and buried when they fell behind early on, as Sterling played in Kane who poked the ball past Georgiy Bushchan.
Ukraine’s giant striker Roman Yaremchuk forced a save from Jordan Pickford and a Declan Rice piledriver was kept out by Bushchan, with England looking comfortable.
However, Ukraine was a different proposition after injured defender Serhiy Kryvtsov was replaced by Dynamo Kiev winger Viktor Tsygankov in the 36th minute.
They finished the first half strongly and more pessimistic England fans may have spent the interval reliving their exit from Euro 2016, when they lost to Iceland in the last 16 despite also having opened the scoring in the fourth minute.
They need not have worried.
England scored again less than a minute after the restart when Luke Shaw delivered a free-kick from the left for Maguire to head in.
Four minutes after that Sterling supplied the overlapping Shaw and he crossed for a rejuvenated Kane to head home.
The Tottenham star nearly had his hat-trick, a stinging volley producing a fine save from Bushchan.
From Mason Mount’s resulting corner came the fourth goal, another header, this time from Henderson, the first of five substitutes sent on by Southgate who would have been thinking about the semi-final long before this quarter-final was officially over.
