How to stop a Blitzkrieg

That's a chapter title in Paul Kennedy's WWII book "Engineers of Victory".  The German Army was all conquering at the beginning of WWII.  They smashed the Poles, the Norwegians, the Belgians, the French, the British and the Russians, bang, bang, bang. The Germans were unstoppable, they beat all comers, hands down.
   Clearly, one of the things the Allied had to do to win WWII was beat the German Army.  Kennedy goes on to some not very satisfactory explanations as to how the Allies finally managed to pull off victories at Stalingrad and El Alamein. 
   Looking at the problem with modern eyes, we would say that the answer to beating the Germans was to use combined arms.  Infantry with tank support, and artillery support and air support.  Not pushing a lone infantry or lone tank unit into action unsupported. 
   Rick Atkinson in his "Army at Dawn" gives examples.  He is telling the story of the US Army in North Africa.  The Americans had recognized the effectiveness of the German Panzer divisions and had organized their own army into well balanced divisions combining infantry, armor, and artillery under a single commander. 
   But in the early days of operations in North Africa, Atkinson tells of repeated disasters after a higher command (corps command usually) would order lone infantry regiments or tank regiments into action, unsupported by division, bypassing the division commanders.  Only later, after about a year's bad experiences like Kasserine pass, would US divisions be ordered into action as intact formations.  And the combined arms divisional operations were much more effective, i.e. they pushed the Germans back, rather than just getting shot up.