On a night to remember in front of almost 60,000 fans, England reached the European Championship final for the first time, though they had to come from behind as a Simon Kjaer own goal cancelled out Mikkel Damsgaard's superb free kick for the Danes in the first half.
The home side were on top throughout but struggled to break down the battling Denmark defence, until they were awarded a penalty in the 103rd-minute after Raheem Sterling went down with minimum contact to allow captain Kane to decide it.
It was a tough way for Denmark to end their emotional ride from the fear and distress of Christian Eriksen’s opening game collapse to their first semi-final since their shock Euro 92 win, but their exhausted players left Wembley with socks rolled down but heads held high.
England will return on Sunday, 55 years after lifting the World Cup there, but they did it the hard way.
They had reached the semis without conceding a goal and it needed something special to pierce their rearguard as Damsgaard fired a powerful, dipping 25-yard free kick over the wall and beyond the diving Jordan Pickford -- the tournament's first goal direct from a free kick -- after 30 minutes. The crowd were stunned, that had not been in the script, and the question of how England would respond to their first real taste of adversity would now be addressed.
The answer was calmly and patiently, as they passed their way back into the ascendancy. Raheem Sterling was denied at point-blank range by Kasper Schmeichel before the 39th-minute equaliser, when Bukayo Saka hit the byline and fizzed over a low cross that Kjaer bundled over his own line in his attempt to stop the ball reaching Sterling.
Schmeichel was on hand again with an excellent diving save to palm away a Harry Maguire header and England began to turn the screw.
However, despite all the pressure and relentless passing and probing around the box, England struggled to carve out a clear opening and the match rolled into extra time.
The extra 30 minutes became a virtual attack v defence exercise, as Schmeichel saved again from Kane and Jack Grealish.
Sterling continued to drive into the box and was eventually brought down by Joakim Maehle for the VAR-reviewed penalty that Kane stuck poorly and Schmeichel blocked, only for the captain to tuck home the rebound.
England then had to negotiate the last 15 minutes and managed it to spark the loudest, and surely most confident rendition of "Football's Coming Home", ever to ring around Wembley.
