Brazil, who were all but assured qualification for the knockout stages after two successive victories, drew 1-1 with France in Washington to top Group B with seven points.
Norway, the 1995 champions who looked far from confident in their defeat by Brazil on Wednesday, recovered with a stunning 7-1 win over South Korea in Foxboro, Massachusetts to finish second behind the Brazilians.
Germany, already through from Group C with six points, secured their third victory in a row by beating Argentina 6-1 in Washington while Canada seized the second qualifying place from the section by overcoming Japan 3-1 in Foxboro.
Russia progressed to the last eight after two opening victories in Group D.
The remaining three nations to go through, from groups A and D, will be decided on Sunday when hosts the United States, Sweden and China are expected to advance to the quarter-finals.
Canada and Japan both went into their match with a chance of finishing second in Group C, and it was Japan who gained an early advantage when Sawa Homare scored after 20 minutes.
But Canada hit back through Christine Latham before halftime and further strikes from Christine Sinclair and Kara Lang after the break took them to their first women's World Cup quarter-final.
Joint leading scorer Katia claimed her fourth goal of the tournament as Brazil settled for a draw with France. Birgit Prinz also notched her fourth of the campaign in Germany's romp over Argentina.
Two goals from striker Dagny Mellgren and two by Linda Ormen relieved the pressure on Norway in their resounding win over South Korea.
Norway will face the winners from Group A in their quarter-final on Wednesday while Brazil meet the runners-up from Group A the same day.
Germany will take on the runners-up from Group D while Canada play the Group D winners. Both ties will be staged on Thursday.