Germany secured their first victory since they crashed out of the 2018 World Cup at the group stage when debutant Nico Schulz's scruffy shot squirmed under Peru goalkeeper Pedro Gallese's body.
Peru had led at the Rhein-Neckar-Arena on Sunday when Luis Advincula stormed past Schulz and squeezed a near-post effort beyond Marc-Andre ter Stegen, and the South Americans had opportunities in the second half too after Julian Brandt had levelled with a cool chipped finish over Gallese.
"I'm glad that we won the game," Germany head coach Low told RTL.
"We felt that the team wanted to win the match, they fought until the end.
"We missed a lot of chances in the first half. That was the problem. The substitutions made the rhythm a bit broken. The balance is not yet 100 per cent."
Low admitted that Schulz could have done better for Peru's goal but was pleased he turned out to be the match-winner.
"I'm happy for him, because he also made a good impression in training and made a very committed game," Low added. "He is physically very good and fast."
Brandt was in Russia for the World Cup, though he featured for just 19 minutes in three substitute appearances.
He started against Peru and showed the kind of creativity and drive that the German attacks were missing in June.
"Beyond the World Cup, I've gained a lot of self-confidence, I feel very comfortable in the national team," Brandt added.
"I try to use every minute and bring in my strengths and I'm happy about my goal."