The centre-back scored his second goal of the tournament to send Joachim Low's men into the last four
The Borussia Dortmund defender missed the last-16 victory over Algeria as a result of flu-like symptoms, with the bug having also affected a number of the squad in the build-up to Friday's game.
Hummels, however, showed now ill-effects of any sickness in the 12th minute, rising highest to head home Toni Kroos' free-kick from the left and hand Germany victory at the Maracana.
Such consistent performers throughout World Cup history with seven final appearances, Germany once again showed their ability to grind out results in major tournaments as they successfully stifled France, though Karim Benzema came close to a leveller late on, only to be denied by Manuel Neuer.
For Didier Deschamps' men, a competition that had promised so much after the group-stage thumpings of Honduras and Switzerland ended in disappointment, as France failed to gain revenge for semi-final defeats to West Germany at the 1982 and 1986 editions.
Germany made the better start, but it was France who had the first effort on goal in the seventh minute when Benzema volleyed Mathieu Valbuena's chipped pass narrowly wide.
Hummels made France pay for that miss five minutes later when he broke the deadlock with his second goal of the 2014 World Cup. The defender beat Raphael Varane to Kroos' set-piece and sent a glancing header in off the underside of the crossbar.
Twice Germany had appeals for penalties waved away, claiming fouls by Mathieu Debuchy on Miroslav Klose and Thomas Muller, but on each occasion referee Nestor Pitana signalled for play to continue.
Neuer was finally called into action for the first time 11 minutes before the break, and reacted brilliantly to keep out Valbuena's left-footed volley, before Hummels deflected Benzema's rebound over the bar.
The striker continued to threaten as half-time approached, seeing his header blocked by the body of Hummels and then firing a strike straight at Neuer after cutting in from the left shortly afterwards.
France cautiously pressed for an equaliser after the break, but Varane's header from Valbuena's right-wing cross on the hour-mark was comfortable for the goalkeeper.
Muller almost put the result beyond doubt nine minutes later, but his shot from an angle was deflected narrowly wide by Mamadou Sakho, although the officials failed to spot the deviation and awarded a goal-kick.
Andre Schurrle replaced Klose - who is still in search of the goal that will see him become the World Cup's all-time leading scorer outright - and tested Hugo Lloris with a low drive that the Tottenham man was equal to.
Benzema worked some space inside the area with 14 minutes to play, but once again Hummels was there to block and Neuer parried away Blaise Matuidi's effort from a tight angle.
With France forced to push men forward, they left themselves vulnerable on the break and Lloris saved well from Schurrle, who ought to have done better eight minutes from time.
Neuer then palmed away Benzema's angled drive late on as Germany held on to seal yet another semi-final berth and send France crashing out.