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.
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.
Benzema went close twice more as France gained some momentum before half-time, and they maintained it after the break as Yohan Cabaye, Paul Pogba and Blaise Matuidi gained control of the central areas, allowing Griezmann and Valbuena to cause damage from wide.
But Germany appeared to realise the increased threat, dropping deeper and limiting France to a Varane header and Matuidi strike that were both comfortably saved by Neuer.
Low introduced Andre Schurrle from the bench and he significantly boosted the tiring Germans, although he might have done better with two opportunities on the counter attack.
[Read Full Article: Germany beat France to reach semi-finals]