The Borussia Dortmund defender was on hand to head past Hugo Lloris on 13 minutes to send his nation into the last-four stage of the tournament, where they will face either Brazil or Colombia.
The build-up to the encounter was dominated by reports that many of the German camp had been suffering with flu.
However, there were no signs of fatigue early on and Joachim Low's side put to bed any rumors of malaise when Hummels nodded them ahead within 15 minutes.
The centre-half, recalled to the starting lineup in place of Per Mertesacker, vindicated his coach's faith in him by out-muscling Raphael Varane to glance a Toni Kroos free kick past Lloris.
Les Bleus slowly grew into the game and fashioned two goalscoring opportunities before the break, with Manuel Neuer producing a tidy save to deny Mathieu Valbuena before Karim Benzema was also thwarted by the Bayern Munich shot-stopper.
Didier Deschamps's side managed to retain that momentum after the break and began the second half strongly, as Patrice Evra beat the offside trap from a free kick but his tame header never tested Neuer.
Having scored the opener, Hummels then denied France a prospective equaliser by throwing himself in the line of fire to block Benzema's close-range effort.
Unperturbed by the missed chance, France continued in the same vein and Neuer was forced to palm away Blaise Matuidi's thumping shot from an acute angle.
Andre Schurrle could, and perhaps should, have put the result beyond doubt in the closing 10 minutes, firing Mesut Ozil's cut-back pass at Lloris following a swift counter-attack from the Germans.
The Chelsea ace was denied again moments later, this time firing against the frame of Varane, but the missed opportunities would not come back to haunt Low's troops as Germany held on to seal their place in the semis for a record fourth successive tournament.
