Sterling, a bundle of energy of invention throughout, was felled on the corner of the six-yard box in extra time after wriggling past a couple of challenges to win a penalty.
Though Harry Kane’s spot-kick was saved by Kasper Schmeichel, the former City keeper could only push the ball back to the Tottenham striker who swept up the rebound.
And Phil Foden gave a late cameo off the bench for the final 28 minutes of a game that was keenly contested from the first minute to the last.
England will now face Roberto Mancini’s Italy in the final on Sunday.
After a cagey opening with few clear-cut chances for either side, the Danes took the lead from a set-piece.
When Luke Shaw pulled Chelsea defender Andreas Christiansen down as a free-kick was floated in from the right, the referee correctly penalised the Manchester United defender.
With another free-kick – this time 20 yards or so from goal – Denmark were given a chance to take the lead, and it was taken emphatically.
Mikkel Damsgaard struck the set-piece over the wall and past Jordan Pickford to make it 1-0 and silence the majority of the 65,000 Wembley crowd with 30 minutes on the clock.
It was the first goal conceded by Gareth Southgate’s side in Euro 2020 and also the first direct free-kick scored in the entire tournament.
England responded well and on 37 minutes, Kane’s excellent pass to Sterling saw the City forward seem certain to score, but Schmeichel was equal to it and kept it out by making himself big and beating the point blank shot clear with his torso.
But a minute later, it was 1-1 as Bukayo Sako broke clear on the right of the box before crossing in a low ball that was turned into his own goal by Simon Kjear with Sterling ready to pounce behind him.
The second-half passed with no clear-cut opportunities for either side.
Stones and Walker were solid throughout – Walker’s mopping up at the back was magnificent at times - though as the 90 minutes ended 1-1, there was still no sign of Foden who must have been champing at the bit to help his country.
As the game entered extra time, the one thing every England fan was hoping to avoid was penalties!
Then, just a couple of minutes into the additional 30 minutes, Foden was introduced to a raucous and enthusiastic reception from the England fans.
The PFA Young Player of the Year was quickly in the heart of the action, buzzing with energy and demanding the ball around the Danish box.
Then, 103 minutes into this epic contest, Sterling’s determination on the right earned the penalty that Kane eventually scored from to make it 2-1 and leave a nation so used to seeing their hopes dashed holding its collective breath.
Could England see out the time that remained to take their place in a major final for the first time in 55 years?
The answer was yes, with Denmark unable to find a way back in as their brave run to the semis was finally ended at Wembley.
Now, only Mancini's excellent Italy stand in the way of England and that elusive first major title since 1966.