Germany, champions in 2003 and 2007, demolished Sweden 4-1 in Ottawa, while China won 1-0 in Edmonton to send the last African challenger Cameroon home.
Forwards Celia Sasic and Anja Mittag both scored their fifth goals of the tournament, with Sasic netting a double, as the top-ranked Germans closed down their fifth-ranked European rivals in scorching conditions at Lansdowne Stadium.
Germany coach Silvia Neid described the victory as "a very important game, maybe a key match" in the tournament.
Germany, who were shocked in the quarter-finals of the 2011 World Cup at home, next play either France or South Korea for a place in the semi-finals.
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While Germany and Sweden battled in temperatures reaching 38 degrees Celsius (100 Farenheit), it was raining in Edmonton, where Wang Shanshan's first half goal was enough for China to set up a meeting with either the United States or Colombia.
China coach Hao Wei had a touchline ban and was forced to watch the game from the stands in Edmonton's Commonwealth Stadium.
"Today all the players were wonderful, they put on a spectacular performance, demonstrating amazing resilience and bravery," said assistant coach Chang Wei-Wei.
"They fought like warriors for over 90 minutes. I want to thank them for their hard work."
The defence of the 16th-ranked Chinese was rock solid allowing few chances for 53rd-ranked Cameroon's energetic forwards.
Once 25-year-old Wang scored her second goal of the tournament it was impossible for Cameroon to get through.