The two matches followed an identical script, finishing 1-1 after 120 minutes before being decided in a shootout. Paraguay goalkeeper Orlando Gill and Morocco's Yassine Bounou emerged as the heroes, producing decisive saves to send their teams through, while Germany and the Netherlands failed to convert under pressure.
Morocco will face Canada in the quarter-finals, while Paraguay will take on the winner of the match between France and Sweden.
Earlier in Houston, Brazil came from behind to beat Japan 2-1 in a hard-fought contest. Japan put in a resilient performance and held Brazil for much of the match, but goals from Casemiro and Gabriel Martinelli completed the comeback and secured a place in the quarter-finals for Carlo Ancelotti's side.
Brazil will next play the winner of the round-of-16 clash between Ivory Coast and Norway.
