Jill Scott put Phil Neville’s side ahead with a fine finish in just the third minute at the Stade Oceane, the earliest goal of the tournament so far and the fastest England have scored at any edition.
Ellen White, having hit the post just before the half-hour mark, made it 2-0 with a 40th-minute tap-in, taking her goal tally in France to five as she moved alongside the United States’ Alex Morgan and Australia’s Sam Kerr as the tournament’s joint top-scorer.
And Lucy Bronze then added a superb third in the 57th minute, smashing a shot past Ingrid Hjelmseth from just outside the box.
Norway, showing more threat in the second half than in the first, came close to pulling a goal back soon after when substitute Lisa-Marie Utland’s shot was cleared off the line by Steph Houghton.
England then had the chance to extend their lead with seven minutes of normal time remaining, but Nikita Parris’s penalty was saved by Hjelmseth – the second time in the campaign she has failed with an effort from the spot.
Neville’s team can now look forward to a last-four clash next Tuesday in Lyon against either hosts France or holders the United States, who meet in Paris on Friday night.
It is the third successive major tournament in which the Lionesses have made the semi-finals, following the runs at the 2015 World Cup and Euro 2017. The bid to go one better than they did in those campaigns and reach a first World Cup final remains on following an impressive evening’s work that could hardly have started any better.
In front of a crowd of 21,111 that included David Beckham, England worked the ball down the right, Bronze cut the ball back, White missed it as she attempted a strike and it ran to Scott, whose low shot went in via the post with just two minutes and six seconds on the clock.
Parris found herself in a good position in the 21st minute but, having opted to shoot rather than pass to White or Fran Kirby, she sent the ball off-target.
Soon after, Scott lost possession in midfield but recovered to block a shot from Caroline Graham Hansen, before White received the ball from Parris and drove it against the upright.
Demi Stokes blocked a shot from Norway midfielder Guro Reiten, whose appeals for handball were rejected, and Parris then saw a header well saved by Hjelmseth.
Moments later England had their second as Bronze worked the ball to Parris and her lay-off was slotted in by White from close range.
Houghton demonstrated her class early in the second half when Isabell Herlovsen headed a cross towards Hansen in the danger zone, the England skipper on hand to intercept and clear the ball away.
Norway applied more pressure, with Houghton again doing well to deal with the threat, before Bronze, meeting Beth Mead’s free-kick, produced the emphatic finish that looked to put the outcome beyond doubt.
Houghton excelled again in the 66th minute when Millie Bright’s poor pass was pounced upon by Utland, who went around Karen Bardsley but saw her shot cleared off the line by the captain.
Bardsley subsequently saved an effort from Herlovsen before a foul on Houghton by Maria Thorisdottir gave England a penalty – but Parris was denied by Hjelmseth.
England coach Neville heaped praise on Bronze. “What you have seen tonight is that Lucy Bronze is the best player in the world: there is no player like her in the world, no player who has her athleticism and quality.
“I played full-back but never to that level she played at.”
Progression means England head to a last-four clash in Lyon, the city where Bronze plays her club football for the Champions League winners.
“I’ve been dreaming of getting to Lyon and playing in that semi-final,” she said.