Steph Houghton and Lucy Bronze scored second-half goals as England rallied for a 2-1 for the win that will send the eighth-ranked nation to Vancouver for a quarter-final matchup with Canada next Saturday.
"The first emotion I'm feeling is a real sense of pride in the team," said England coach Mark Sampson. "To show that character and resilience to come back from a goal down at this tournament is an incredible achievement.
"This is a huge win, not just for our team but for all of England."
After a near fatal giveaway in the first half, Bronze took a shot from just above the penalty box and beat Norwegian 'keeper Ingrid Huelmseth in the 76th minute with the eventual winner.
Solveig Gulbrandsen had given Norway a 1-0 lead early in the second half, but the Norweigians were unable to produce after that.
No. 11 Norway celebrated when Gulbrandsen got her head on a corner from teammate Lene Mykjaland and put the ball just barely across the England goal line in the 54th minute.
Up until that point, it was Norway that had been carrying the play against the higher-ranked English side.
But as much as the field seemed to be tilted in Norway's favour up to that point, a quick strike by England in the 61st minute tied the match 1-1 and gave the Lionesses the momentum.
"There were two different halves," said Norway coach Even Pellerud. "A dominating, very strong first half from my team, but problems capitalizing on the chances hurt us. The second half also started very well. But that said, when England scored on their first chance of the second half to tie the game we started to struggle.
"Complements to my English colleague who managed to do some really nice tactical changes at halftime. It was a good job by the coaching staff of England."
On the tying goal Houghton tucked a header just inside the post past Huelmseth, who had seen far less action up to that point than her counterpart Karen Bardsley.
Huelmseth did make a terrific diving stop in the 80th minute to keep that match at a 2-1 difference.
While the opening goal was her first real test of the second half, Bardsley kept the game scoreless into halftime with some key stops.
"We've got to give big credit to Norway. I thought particularly in the first half they caused us some problems and probably were fortunate to be coming in nil-nil at the half," said Sampson.
Norwegian forward Isabell Herlovsen was sent in all alone on Bardsley with a beautiful ball, but England's 'keeper charged out quickly from her goal and made a save with Herlovsen bearing down in the 12th minute.
Bardsley got some luck when midfielder Kristine Minde got in behind the defence, but put a shot just to the outside of the post.
Ada Hegerberg got in alone in the 39th minute only to be stopped by Bardsley, who again raced from her net to take away any angle to minimize the scoring chance.
"They're prolific goal scorers and I have a lot of respect for what they've done, but I think it comes down to moments and fortunately for me things seemed to slow down," said Bardsley.
"I just seemed to be in the right frame of mind to be as big as possible and be in the right spot at the right time."
Bardsley was rewarded with the FIFA Player of the Match.