The three-time champions needed extra time to beat Algeria in the last 16 and suffered a bout of illness in midweek, but they were comfortable victors over a disappointing France in Rio de Janeiro.
Hummels got the better of Raphael Varane to score what proved to be the winning goal and Germany can now prepare for a meeting with Brazil in Belo Horizonte on Tuesday after the hosts beat Colombia.
Chris Waddle analysis
“France fell short. They looked entertaining in the group stage but were beaten by a better team, with more experience at this level, who knew how to see out the game. Germany dominated the midfield and dictated the pace of the game, while France were well off their own pace.”
Germany goalkeeper Manuel Neuer gave another faultless performance and Joachim Low’s men deserved their win against a France side who failed to hit the heights of earlier in the tournament.
It is 60 years to the day since Germany overturned a two-goal deficit to upset Hungary in the 1954 final, and this will go down as another memorable day in their history.