Popp, winning her 100th cap, and Sara Daebritz netted in quick succession in the first half with Lea Schueller wrapping it up late on to set up a meeting with Sweden or Canada.
Popp headed home after 20 minutes and Daebritz doubled the tally with a penalty seven minutes later, with VAR being used for both goals. Schueller added the third on 86 minutes as the African champions ran out of gas.
The only team along with the U.S. not to concede a goal in the tournament, Germany have now reached the last eight at every women’s World Cup.
"That first goal gave us some safety, but then we allowed Nigeria to get back into the game a little bit. After the break, we were very dominant," said player-of-the-match Popp.
Dzsenifer Marozsan, recovering from a foot injury, started on the bench but the Olympique Lyonnais player was confident she would soon be ready to play.
"Now I might even be able to come back. It will remain painful for weeks, but I am not scared," she said.
"I probably cannot play an entire match but I was happy I was not needed today."
Germany controlled the midfield against the Nigerians and were quickly rewarded.
Popp broke the deadlock from Lina Magull’s corner, the goal being awarded after a VAR review ruled there was no offside.
Magull was then brought down by Evelyn Nwabuoku and VAR confirmed the penalty call before Daebritz coolly converted.
Nigeria offered more of a challenge after conceding the second goal and came close to reducing the arrears early in the second half when substitute teenager Rasheedat Ajibade burst down the left flank in impressive fashion only for Desire Oparanozie to just fail to connect with the cross.
Forward Popp dropped down to midfield as Germany protected their lead and Schueller intercepted a poor back-pass to make it 3-0 with a clinical finish eight minutes from time.
"I think we showed the whole world that Nigeria have a team that has improved a lot," said Nigeria coach Thomas Dennerby.
"Of course you’re not satisfied to go out but you also have to recognise where we came from – and we’re just not ready yet."
(Reporting by Julien Pretot; Editing by Tony Lawrence)
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