David Beckham was among the crowd at the Stade Oceane to see midfield stalwart Jill Scott open the scoring inside three minutes of this quarter-final, becoming just the second English player to score at three separate women's World Cups.
Ellen White grabbed her fifth goal of the tournament five minutes prior to half-time and Bronze made sure of the victory with a rising shot high into the net as the hour mark approached.
England were so comfortable towards the end that they could even afford to squander a penalty, Nikita Parris having her late spot-kick saved.
There were striking similarities between Bronze's effort here and her goal that gave England a 2-1 win over the same opponents at the 2015 World Cup.
The Lionesses went out of that tournament in the semi-finals and also fell in the last four at Euro 2017. Now they will hope to go a step further, although a daunting challenge awaits against hosts France or holders the United States in Lyon next Tuesday.
"We are a team that has lost in the semi-finals of the last two major tournaments and I suppose the main reason I was brought into this job was to get us through a semi-final," Neville said.
"What I said to them at the end, and I am not ashamed to say it, was 'are you ready to win a World Cup', because we are in it to win it and I think we are in good shape."
France and the USA meet in a blockbuster quarter-final in Paris on Friday, but Neville insisted his team are not afraid of what awaits them next.
"Both teams hold no fear for my players. We actually said when we qualified against Japan that that we were in the best side of the draw because of this semi-final.
"My players and I want the biggest games and this will be the biggest game of the World Cup."
Norway had ousted Australia on penalties in the last round, but this was a step too far for a team who came to France without their superstar striker Ada Hegerberg.
"We lost against a better team than us," admitted coach Martin Sjogren. "Of course we believed we could hurt England, but at this stage of the tournament all teams are very, very good."
- Landmark goal for Scott -
They could not recover after falling behind to Scott's early goal, with the outstanding Bronze charging forward down the right and cutting the ball back for the Manchester City midfielder to side-foot in off the far post.
It was a landmark goal for Scott, who first found the net for her country against Argentina at the 2007 World Cup.
England looked like scoring every time they came forward in the first half, with White hitting the post before the second goal came on 40 minutes.
This time Parris teed up White to convert from inside the six-yard box and join Australia's Sam Kerr and Alex Morgan of the USA at the top of the World Cup scorers' chart.
Any hopes Norway had of a second-half comeback were doused in the 57th minute when Bronze was fouled on another charge forward. Substitute Beth Mead laid the ball back to Bronze from the resulting free-kick, and the Lyon star smashed home in style.
England then stood firm to secure a fourth straight clean sheet, although they missed the chance to score a fourth goal from the spot with seven minutes left.
Captain Steph Houghton was shoved over in the box by Maria Thorisdottir, but Parris saw her kick from 12 yards kept out by Ingrid Hjelmseth.