Trailing 1-0 going into the last five minutes of regulation time, Enzo Fernandez and substitute Lautaro Martinez scored for Argentina.
Anthony Gordon had given England the lead, but Lionel Messi and Co. had other ideas.
Argentina pushed for an equalizer and the pressure eventually led to Fernandez scoring in the 85th minute. Martinez headed in the winner two minutes into injury time.
The game resumed one of the biggest rivalries in international soccer and there was a raucous atmosphere in the stadium even before kickoff as both sets of fans tried to drown out the other team's national anthem.
Argentina will play Spain in the World Cup final on Sunday in East Rutherford, New Jersey.