Mats Hummels headed Germany into a 12th-minute lead at the Maracana, glancing Toni Kroos' free-kick in off the underside of the crossbar beyond a helpless Hugo Lloris.
From that point on, Joachim Low's men were happy to nullify any France attacks and saw the game out in relative comfort, Manuel Neuer's stoppage-time save from Karim Benzema a rare moment of concern.
The win propelled Germany into a fourth consecutive World Cup semi-final, and captain Lahm was unconcerned by the way they secured victory.
"We're in the semi-finals so who cares about anything else," he told German television.
"It wasn't easy today, especially not in the sun, but we worked well as a team and the team comes first.
"We should maybe have made it 2-0. We wasted a great counter-attack, so that meant it remained tight to the end, but it was a good performance for us and we're in the semis.
"It was a 50-50 game, but we got the goal first and then they had to come at us.
"This is a quarter-final of a World Cup and you never play against a side who have no chance against you."
Match-winner Hummels, meanwhile, hopes the side can put semi-final defeats in 2006 and 2010 behind them and make it to their eighth World Cup final.
"This is the next dream to have become reality and the next positive moment here in Brazil and I hope it's not the last either," he said.
"I hope it's not over now and that we can manage to win again in five days' time."
