England had led since the 55th minute through Anthony Gordon, who cut inside to finish first time after a superb cross from Morgan Rogers. The lead held until deep into the second half, with Jordan Pickford producing a string of saves to repel wave after wave of Argentina pressure. Alexis Mac Allister then crashed a header against the post from Rodrigo De Paul's cross as the holders continued to push.
The breakthrough finally came in the 85th minute, when Enzo Fernandez drilled a stunning strike from distance beyond Pickford to level the scores. Lionel Messi, who set up both Argentina goals, then found Lautaro Martinez two minutes into stoppage time, and the substitute headed home the winner to complete the turnaround.
Argentina will now face Spain in Sunday's final as they defend the title they won in 2022, while England must contend with a third-place play-off against France on Saturday.
Match-winner Martinez struggled to contain his emotions afterwards.
"Truly I don't know what to say. It is very overwhelming. I always dreamt of this moment with the national team, since my Dad bought me my first pair of boots," he said. "This for me means more than just a goal, to be in a final...
"I have my kids here with me, they have helped me to slow down. Just an unforgettable moment, one that we need to enjoy. Today I am a man enjoying life. Enzo scored an amazing goal too. I'm calm and assured because this team continues to show what it's made of. They got tired. They had pressed for 60 minutes and they could not give more.
"We started to push and we got momentum because we were calmer as took more control of the ball and got higher up the pitch. In the end we got the two goals, and three and a half years on we're in another World Cup final."
Argentina head coach Lionel Scaloni was similarly emotional at full-time.
"Well, I'm lost for words. A great happiness for our country and our people. And another great happiness for this group who never stop surprising me and never know when they are beaten," he said. "I can tell them that we are going to try to win, we're going to leave it all out there, but the truth is that to do this is very difficult. It's very difficult for people to understand what our players have given. It is so impressive. We are unique. It's not arrogance, it is all heart. Today so many people arrived here to support us and for that I am truly grateful - they helped us to victory. This shirt merits us giving absolutely everything possible until the very end. To not spare anything at all."
For England, the defeat raised questions over a series of defensive substitutions made by head coach Thomas Tuchel as his side sat deeper in search of the win, but he insisted afterwards he had no regrets.
"We keep on going with the contract until the home Euros. I'm looking forward to that even though right now it's difficult to look that far ahead," Tuchel said. "Of course, it's a semi-final; a lot of big football nations are eliminated before the semi-final, so it is an achievement. No-one wants to hear that at the moment; me neither because we demand the most of ourselves. That's just the nature of being competitive."
Despite the manner of the defeat, England's run to the last four will be viewed internally as a positive step, with the semi-final representing their best World Cup showing since their triumph on home soil 60 years ago, and a win over France on Saturday would extend that best finish since 1966 further still.