Teenage midfielder Giulia Gwinn scored the only goal for Germany, for whom Lena Oberdorf became her country's youngest World Cup player at 17 years and 171 days.
In the later match in Group B, Jenni Hermoso converted two late penalties as Spain won for the first time at a Women's World Cup, rallying to beat a South Africa team that finished with 10 players.
The Germans complained after their game in Rennes that the Chinese had aimed for their ankles.
"They were often late in the tackles and kept catching our feet," said German captain Alexandra Popp. "We had to really grit our teeth."
Coach Martina Voss-Tecklenburg said she had not been sure at one stage if star Dzsenifer Marozsan would finish the match.
"A lot of our players were caught on the ankle today, and it doesn't look good for some of them. What Dzseni Marozsan suffered today was brutal."
"We were a little surprised by the assertive approach of the Chinese, but it's a competitive game, not a friendly, " she said.
The Germans took the lead after 66 minutes.
The Chinese cleared a corner to the top of the penalty area where Freiburg's Gwinn had time to take a touch before smacking a shot that curled between the on-rushing Yang Li's legs and into the corner of goalkeeper Peng Shimeng's net.
"I am very happy to have scored a goal at the World Cup," said Gwinn, who also struck the opening goal when Germany beat China in the group stage of the under-20 World Cup down the road in Saint-Malo last August.
Germany, two-time winners of this competition, dominated possession and territory, but their goal twice survived narrow escapes.
China's crisp passing carved out two dangerous chances for Yang in the first half.
First she took an extra touch in front of an empty net and with Sara Doorsoun rushing at her, shot wide.
Just before half-time, Yang beat goalkeeper Almuth Schult, but hit the inside of the post.
"There was a lot of pressure on our defence, but in our attack we created opportunities," said Jia Xiuquan, China's coach.
"Compared to Germany we are not at the same level, but it does not mean we cannot fight."
Shock lead
In Le Havre, South Africa took a shock lead with their first ever shot on target at a Women's World Cup.
Thembi Kgatlana, who plays for Beijing BG Phoenix in China, curled a right-foot shot into the top corner to give South Africa the lead.
Spain dominated possession, but a combination of resolute South African defending, solid goalkeeping from Andile Dlamini and Spanish wastefulness meant Banyana Banyana still led with 20 minutes to play.
Then Hermoso's ball into the box struck Janine van Wyk's arm, the South African captain was punished with a yellow card and a penalty kick. Atletico Madrid striker Hermoso waited for Dlamini to go the wrong way before slotting the ball into the corner.
With nine minutes left, Nothando Vilakazi cleared but caught Lucia Garcia with the follow through. After a VAR review, Vilakazi saw a second yellow card and Spain had a second penalty. Hermoso became the first woman to score from two penalties at a World Cup.
"When you have a penalty in a World Cup with a chance to tie the game, nerves are going to be there. I told myself I as taking shots in the park by my house," said Hermoso.
"Luckily the first went in but the second was even more complicated because it could mean the victory in this game. I just tried to hit the net and that was it."
"Even though we haven't played well or how we would like, we've won," Hermoso said. "We are aware that we're in a World Cup and it's not going to be as pretty as we might have dreamed."
Garcia added a third in the final minute, rounding Dlamini and shooting into the empty net.
"We had a very good first half." said Kgatlana. "But in the second half we started getting tired."
The defeat means South Africa have lost all 10 of their games this year.