Norway defender Ingrid Engen diverted Hinata Miyazawa's cross into her net to give the 2011 winners the perfect start.
Norway, though, leveled a few minutes later when Guro Reiten scored.
Risa Shimizu's badly deflected shot restored Japan's lead before Hinata Miyazawa sprinted through to score a third and clinch her team's victory.
The goal secured Japan's participation in the quarterfinals and put Miyazawa on track for the Golden Boot, with five goals in Australia and New Zealand.
Norway was second-best for much of the game, but goalkeeper Ayaka Yamashita saved Karina Saevik's bullet header to set up an entertaining finish.
In the last eight, Japan will face either the reigning champions, the United States, or Sweden.
Japan is vying for its first Women's World Cup crown in 12 years, and they have scarcely missed a beat in this competition.
They breezed through the group stage, winning 4-0 against fellow quarterfinalists Spain in their last group game.
They played fantastic counter-attacking football in the game, winning despite having just 23% possession to demonstrate their ability to dig in and grind out a victory against a strong opponent.
Job done for #JPN! 😎@JFA_Nadeshiko | #FIFAWWC
— FIFA Women's World Cup (@FIFAWWC) August 5, 2023
Reiten's goal is their first of the World Cup, but aside from that header, they put up another excellent defensive performance.
Yamashita was there to produce an outstanding save whenever their resistance was breached.
Norway had hoped to reach the quarterfinals of a Women's World Cup for the second time in a row, but they struggled in 2023.
The 6-0 triumph against the Philippines in their last group game broke a six-game losing streak, but Japan was always going to be a tougher test.
Norway's chances in this tournament have been hampered by an injury to star forwards Ada Hegerberg, who had not played since the 1-0 loss to New Zealand in their opening game until coming off the bench on Saturday.
She entered the game with 16 minutes remaining but did not affect the outcome.
Even a completely fit Hegerberg is unlikely to have made much of a difference against Japan, who had their opponents pinned back within their own half for practically the entire second half.