Norway took the lead in the 36th minute through Andreas Sheldaraj, giving their side a 1-0 advantage before halftime.
England responded early in the second half when Jude Bellingham found the equaliser in the 47th minute, bringing the score level at 1-1.
With both teams unable to find a winner during regular time, the match went into extra time.
Bellingham once again proved to be England's hero, scoring his second goal of the match during extra time to seal a dramatic 2-1 victory and send the Three Lions into the semi-finals.
England will now face the winner of the quarter-final clash between Mexico and Switzerland in the semi-finals, which is scheduled to be played on the 15th.