Maier launched a shot from the right side in the 53rd minute to beat Canadian 'keeper Erin McLeod.
The seventh-ranked Canadians have never beaten Germany, but had to have been pleased with their performance against the world's No. 2-ranked team.
Germany had averaged three goals a game against Canada in the previous 10 meetings between the two teams.
Canada held the Germans scoreless for the first 45 minutes for the first time in its history.
"I think there were some real positives in there today," said Canadian head coach John Herdman. "Defensively, we were able to hold them and there was some real resilience from the girls."
Added captain Christine Sinclair: "John Herdman has us believing that we can beat any team."
The Germans outshot Canada 19-4 in front of 9,781 fans, and had an 8-2 advantage in shots on target. The Germans took 15 corner kicks, while Canada had none.
"We'll keep working. There is still some time left to catch these Germans," Herdman said. "All in all, we had some good lessons. I am proud of the girls today."
Two players made their debut for Canada's senior women's side — forward Melissa Busque started the game, while Rachel Melhado came on at centre back in the 72nd minute.
Substitute Danica Wu made her second appearance.
"Throughout the game, I got more and more comfortable," Busque said. "I am super happy. I know there is more to come."Suggest a correction