The contest between the two European powerhouses lacked spark and Hummels’s 13th minute strike spelt doom for France at the iconic Maracana stadium.
Germany keeper Manuel Neuer was also outstanding under the bar as he made two spectacular saves in each half to deny France the equaliser.
Neuer also made a last-second save when he pushed Karim Benzema’s strong left-foot strike from the left to send his side into the World Cup semi-finals for fourth successive time.
Germany had more possession but it was France, who had first strike in the rival goal post in the seventh minute but Benzema could not provide the finishing touch as he hit a volley wide on a pass from Mathieu Valbuena.
The Germans were clearly the more dominating side and they were rewarded for their effort as Mats Hummels headed home a superb free-kick from the left taken by Toni Kroos.
Hummels not only jumped well but also out-powered French defender Raphael Varane, nodding home the lead in the 13th minute.
The Germans continued to enjoy great possession thanks to to some superb work by their midfield trio of Toni Kroos, Sami Khedira and Bastian Schweinsteiger.
A rattled France upped their game and swung to action. Again it was Mathieu Valbuena from the left, making a superb effort but Germany keeper Neuer stuck his left arm out made a great save.
Germany also survived the resultant corner as Mahadou Sakha headed over the cross bar.
Veteran Germany striker Miroslav Klose was handled pretty badly as he was taken down a number of times by the French defenders.
Klose also sought a penalty on one such tackle but the referee did not oblige. France improved near the break. Benzema started to find holes in German defence.
The Real Madrid player rushed from the left took a pass from Paul Pogba but his feeble shot landed safely in Manuel Neuer’s arms.
The French side was different in the second half, which was far from the German domination. Antoine Griezmann and Valbuena were staying up as close to Benzema as possible.
Germany midfielder Sami Khedira was shown the first yellow card of the match as he brought down Griezmann, nine minutes into the second half.
The French side raided more even as efforts did not bear fruit. Their midfielder Blaise Matuidi rushed forward with a superb sprint but his cut-back from the left wing was well intercepted by a sliding Bastian Schweinsteiger.
German keeper Neuer came to action first time when he easily picked a header from Raphael Varane.
A couple of substitutions followed as Chelsea player Andre Schurrle replaced Klose for Germany while France brought in Arsenal centre-back Laurent Koscielny in place for Mamadou Sakho.
France did succeed in creating a few half chances but never got that equaliser. Schurrle had a chance to double the German lead but his low shot was was blocked by Raphael Varane.