The highly-rated Germans saw off Nigeria 3-0 in Grenoble in a game which was dominated once again by the role of VAR.
Alexandra Popp's header gave Germany the lead in the 20th minute, and the goal was only allowed to stand after a lengthy wait before referee Yoshimi Yamashita decided Svenja Huth was not interfering in play while in an offside position.
Then, following another VAR check, the Japanese official awarded a penalty, having ruled that Evelyn Nwabuoku had fouled Lina Magull.
Sara Dabritz converted from the spot before Lea Schuller fired in a late third for the two-time champions to seal a quarter-final berth for the Germans who will meet either Canada or Sweden.
VAR also loomed large as Norway ovcercame Australia 4-1 in a penalty shoot-out in Nice after the sides had drawn 1-1 over 90 minutes and extra time.
Ingrid Systad Engen hit the winning penalty as Norway beat Australia 4-1 in a shootout in Nice to reach the Women's World Cup quarter-finals.
Isabell Herlovsen put Norway ahead in the first half before Australia were awarded a penalty which was overturned by refere Riem Hussein after a lengthy video assistant referee review.
Elise Kellond-Knight equalised from a corner seven minutes before time before Australia's Alanna Kennedy was sent off in extra-time.
The game was eventually settled by a penalty shoot-out with the Norwegians emerging triumphant with Australia captain Sam Kerr – who scored four goals in midweek, amongst those to miss her penalty.
Sunday’s action sees Manchester City skipper Steph Houghton and her England colleagues take on Cameroon at 4.30pm in Valenciennes with the winners of that last 16 tie to meet Norway in the quarter-finals.
Sunday’s other tie features Brazil who play hosts France in Le Havre in an eagerly-anticipated match which kicks-off at 8pm.