Player-of-the match Popp broke the deadlock after 20 minutes in the picturesque Stade des Alpes as she nodded neatly home from a Lina Magull corner.
But once again VAR was called upon to validate the goal as her teammate Svenja Huth appeared to be standing in the goalkeeper's eye line in an offside position as the ball found the net.
After a lengthy delay, referee Yoshimi Yamashita allowed it to stand and Germany never looked back.
Nigerian defender Evelyn Nwabuoku fouled Magull in the penalty area with an ugly mistimed kick, again Yamashita turning to VAR to review the incident, before Sara Dabritz slotted home the 27th minute spot kick.
It was Dabritz's third goal of the tournament and left Nigeria needing a minor miracle to retrieve the situation.
The African underdog started the second half with its best opening of the last 16 match as teenage substitute Rasheedat Ajibade burst down the left and sent a shot across the goal, with Desire Oparanozie close to getting a touch.
However, the promising Lea Schuller wrapped it up with the third for Germany after a defensive mistake by the tiring Super Falcons. She seized on a backpass by Halimat Ayinde to blast home with eight minutes remaining of a hard-fought encounter.
The Germans now look to either Sweden or Canada, who play Monday, in the last eight with Martina Voss-Tecklenburg's side yet to concede a goal in four games at the 2019 World Cup.
The 28-year-old Popp could not have been happier with the outcome as Germany also kept its record of reaching the quarterfinals or better of every FIFA Women's World Cup that has been staged.
"It was a perfect day today. We put a lot of pressure on the Nigerians and the early goal gave us stability," Popp told broadcaster ZDF.
Coach Voss Tecklenburg added: "I am so happy for Poppi. It was a special game for her today, and she gave absolutely everything,"