The three-time European champions, among the title favourites, dominated with a performance that was a marked improvement on their 5-3 defeat by Switzerland on Saturday.
However, they wasted close to a dozen clear chances on a rainy evening in Leipzig as they prepare for the finals being co-hosted by Poland and Ukraine.
"We can say this was a decent final test of our preparation and will give us a bit of a boost," said coach Joachim Low, who is leading Germany for a third major tournament.
"Obviously not everything worked well yet. It is clear we could have scored more goals but to go with a win into next week is good for us," he told reporters.
"We will improve, the tempo at the tournament will be higher, in the second half we squandered six or seven chances... so there is still a bit to work on."
"We had some good combinations, allowed nothing to happen at the back," said Lahm. "We [Bayern players] had not played for 12 days, we had only three days of training with the team so not everything can work instantly. That's normal."
"We'll be fully fit when the tournament starts," added Lahm who along with his club team mates had been given some rest after losing to Chelsea in the Champions League final.
