In Utrecht, Babett Peter scored from the spot on 10 minutes and captain Dzsenifer Marozsan converted another penalty in the 56th minute to hand a dominant Germany victory.
Peter converted her second penalty in two games after Daria Makarenko brought down Mandy Islacker in the box, while Marozsan punished Margarita Chernomyrdina's foul on Sara Dabritz.
Germany put Russia under heavy pressure early on as newcomer Sara Doorsoun-Khajeh tested Russian goalkeeper Tatiana Shcherbak with a long-range blast in the build-up to the penalty.
Bayern Munich midfielder Dabritz had two good chances in the first half but Shcherbak foiled her the first time before she shot narrowly wide of the target.
The 19-year-old Shcherbak also tipped Peter's header onto the crossbar on half an hour.
In the second half, Anja Mittag flicked the ball just past the post while Marozsan's volley was repelled by a diving Shcherbak.
Peter said she was happy that Germany had made it to the quarter-finals.
"We are group winners with seven points and that was our goal from the start," she said.
"We had a lot of chances today. Against Denmark there might be less chances, but we will have to try to convert them then."
Russian coach Elena Fomina said the game may have been more interesting without the penalties.
"Germany had most of the ball possession and that meant that we were not able to attack and create much danger in front of their goal," she added.