How does exercise play a key in controlling blood sugar highs?

Gets sugar in cells. This causes the body to work and draw upon its reserves. Reserves are in the form of carbohydrates, fat and glucose. Fat gets broken down, as do carbohydrates, and ultimately ends up in the blood as glucose, which supplys the cells. Exercise draws on this supply because the cells do more work, and so glucose is removed from the blood. It is replaced by glcose from your reserves, that go down.