We reveal unexpected origins of age induced departure from 1/f-type temporal scaling in healthy human heart rate. Contrary to the widely established view, we provide evidence that age induced dynamical imbalance in the autonomic control is not due to the emergent functional dominance of the sympathetic nervous system (SNS), but due to emerging (age dependent) relative dynamic dominance of the parasympathetic nervous system function. In particular, we demonstrate that the age induced alterations of healthy heart rate dynamics asymptotically resemble those in so-called primary autonomic failure with neurogenic SNS dysfunction and in other neurodegenerative disorders, including Parkinson's disease even without known autonomic abnormalities. Based upon this, we propose a novel picture of "autonomic aging," characterized by an insufficiency of the SNS function to cope dynamically with various environmental stimuli.