hi! here are a few previous posts on related questions to get you started

Why is German Engineering 'a thing?'

How did Germany overtake Britain in industrial output by the early 20th century, despite the former's lead and straightforward advantages?

What led to the German scientific powerhouse of the 20th Century?

This may not be the full answer, but I'm sure this is a contributing factor: automobiles

Karl Benz is widely considered the first person to invent the self-propelled, combustion-engine automobile in the late 1880s. This is contested to some degree as other German inventors were working on similar projects at roughly the same time. Other German companies soon followed into the car-making market: Diamler, Mercedes, Benz, Porsche, Opel, Audi, BMW, VW. By 1940 all of these brands existed and were a source of great pride for the German public--especially as racing became more and more popular throughout Europe. (sources: The Automobile Book by Ralph Stein, and a few visits to the Mercedes-Benz Museum in Stuttgart and the Technikmuseum in Speyer.)

Germany has a history of engineering/invention that goes back much further than that, even. So the answer to your question may be out there somewhere still, but this might be a good place to start.

Germany had a good education system, Wilhelm von Humbold reformed the Prussian Gymnasium in the 1830's, also since the end of the 19th century they had the Realgymnasium which did stress an education in natural sciences, at a time when it was all Latin and humanities in other countries. [3]

Krupp had a big influence, they built huge steel works and were the first to push for steel canons - the French army still used canons made of bronze, these were of no match during the French Prussian war. See [1] more about the story of the Krupp works. In the late 19th century these corporations (Krupp,Thyssen, Simens etc) became export oriented, because the German market was to small for them.

Also since 1879 in the aftermath of the panic of 1873; Germany instituted tariffs [2] to protect its industry; this had the effect that huge trusts formed (with the aim of price fixing) and these gained lot of influence. However bad, these big firms also had a budget for research and development; Interesting that Hayek mentions that in Britain the introduction of protectionist measures (1931) also led to the formation of monopolies/trusts [4]

Many smaller firms could thrive in an ecosystem around these big trusts. Today these small/medium firms are very important, these are very specialized and are employing around 70% of the workforce (aka Mittelstand)

Also universities were pretty good; they were the leading universities of the world, up until the Nazis. After that refugee Professors from Germany filled American universities (Einstein was the most famous one)

[1] http://www.amazon.com/The-Arms-Krupp-Industrial-Dynasty/dp/0316529400

[2] http://de.wikipedia.org/wiki/Gr%C3%BCnderkrach

[3] http://de.wikipedia.org/wiki/Gymnasium#Entwicklung_der_Gymnasien_im_deutschsprachigen_Raum

[4] Hayek, 'the road to Serfdom' http://m.friendfeed-media.com/07672588579eff7a2ec87e0ea053be31c7db0757

[5] http://en.wikipedia.org/wiki/Mittelstand

It goes well back before World War II. The Germans have a long history of perception by other countries as militaristic and efficient. What's more, the German university system (which America largely adopted) led to strong ties between academic science and industrial science, and combined with encouragement of cartels, Germany was a world leader in lots of scientific and technical fields through the nineteenth century and even further back. In chemicals, for example, German cartels (IG Farben being the most famous name) controlled most of the world's chemical industry going back a long ways. Meanwhile, anyone who wanted to really make a name in chemistry, physics, or lots of other sciences from any country would almost have to spend some years in Germany studying in their labs, as German superiority was pretty widely accepted.

Some people argue that the lack of an empire to spend their money/energy on drove the Germans to invest in internal development instead, though that's more conjecture and interesting idea than historical 'fact.'

In any event, you can find British people bemoaning the 'clever Huns' at least as far back as the nineteenth century. I don't know exactly when it starts, but it's not new. If anything, the real impact of WWII was cementing America's place as the world's scientific and technical leader for the subsequent decades, replacing Germany. World War I also hurt German science/technology, as the anti-German sentiment led to exclusion of Germans from lots of international scientific groups in the interwar years. Germany's prestige mostly survived that time, though.