Gareth Southgate's team dominated the first half, and they had Croatia on the ropes for lengthy periods after Trippier's fifth-minute free kick had given England the lead.
With 68 minutes gone, things were level. Croatia played three straight extra-time matches - two ended in penalty kicks.
Although Russia's Denis Cheryshev and Portugal's Cristiano Ronaldo are also on four goals, they have left the tournament, leaving Lukaku and France's Antoine Griezmann and Kylian Mbappe (three goals each) to battle Kane for the Golden Boot.
The 28-year-old has not tasted defeat in an England shirt since the last World Cup four years ago, going on a 30-match unbeaten run that is the longest of any player in the country's history.
"Thank you England for the best World Cup of my life so far".
"We've played five hard games and I know they are exhausted but there can't be any excuses", he added.
Eric Dier insists England will still play on the front foot against Croatia, despite the strength of their World Cup semifinal opponents.
It was their 12th goal of the tournament and ninth from a set-piece, but they should have added more from open play as they revelled in the space they were being given and looked completely in command.
While Croatia possess arguably the best central midfield pairing in the tournament in the shape of Real Madrid'sLuka Modric and Barcelona's Ivan Rakitic, Southgate's language does not indicate he is about to bring in Eric Dier as an additional defensive midfielder alongside Jordan Henderson. Shortly after, Perisic scooped the ball over the bar with Pickford out of position.
"I agree Croatia has several more experienced players", Juventus forward Mandzukic said.
The match then went to extra-time, and Mandzukic gave his team the lead 19 minutes in, running onto a headed pass from earlier goalscorer Perisic and smashing a low drive past EnglandgoalkeeperJordan Pickford. Suddenly, England was rattled and Croatia was resurgent.
"Until they scored [the equaliser] we were always under cosh", Kane said.
Gareth Southgate and England are ready to face the music.
"We created some good chances when we were 1-0 up, maybe we dropped a little too deep but we didn't get enough pressure on the ball". They even found time to cure a deep-seated psychological hangup about penalties with England's first-ever shootout win at a World Cup.
The victor of England-Croatia will face off with France on Sunday night in the Moscow showpiece, and Southgate will be desperate for his side to get there.
The phrase "It's coming home, it's coming home" became the rallying cry for England fans this week as their chances looked good.
Reassured by positive reports from the tournament and inspired by the unexpected progress of their team, some England fans have raced to Russian Federation in recent days, with extra match tickets released by organisers Fifa and additional seats provided on Moscow-bound flights from Britain.