England goalkeeper Jordan Pickford was beaten for the first time in the tournament when Mikkel Damsgaard converted a stunning 30-yard free-kick.
That left Three Lions supporters fearing the worst – another major tournament semi-final disappointment to go alongside the loss Southgate’s men suffered against Croatia at the 2018 World Cup.
But Denmark captain Simon Kjaer put through his own net under pressure from Raheem Sterling before half-time and, although mounting England pressure could not settle matters inside 90 minutes, the Manchester City forward won an extra-time penalty.
Kasper Schmeichel saved Harry Kane’s spot-kick but the England skipper converted the rebound top send his country into their first major final since 1966.
“I’m so proud of the players. It’s an incredible occasion to be a part of, the fans were incredible all night,” Southgate told ITV.
“We told the players that they would have to show resilience and come back from some setbacks, and we did that.
“I felt we would get over the line but knew we would have different sorts of battles. Denmark are so underrated as a team, they did cause us a lot of problems.
“When you have waited as long as we have to get through to a final, given the limited amount of international experience some of the players have, they have done an incredible job.
“The most pleasing thing is that we’ve given our fans and nation a fantastic night, and the journey carries on for another four days.
“For the team to come through this sort of a night… we suffered in Moscow on a night like this, we managed to put that right.”
Italy await at Wembley on Sunday, with Southgate fully aware that Roberto Mancini’s in-form side represent a formidable obstacle after they overcame Spain on penalties.
“We’re in a final, we’ve got to enjoy that fact, but there is one more massive hurdle to try and conquer,” he said.
“Italy are a very good side, they have really shown outstanding form, have defensive warriors at the back. It’s going to be a great game to look forward to.”
Southgate added: “We’ve had three memorable games on the bounce. We said we wanted to create memories for our nation, now we’ve got to finish the job.”
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