While a large body of research has focused on the study of within-brain physiological networks (i.e. brain connectivity) as well as their disease-related aberration, few investigators have focused on estimating the directionality of these brain-brain interaction which, given the complexity of brain networks, should be properly conditioned in order to avoid the high number of false positives commonly encountered when using bivariate approaches to brain connectivity estimation. Additionally, the constituents of a number of brain subnetworks, and in particular of the central autonomic network (CAN), are still not completely determined. In this study we present and validate a global conditioning approach to reconstructing directed networks using complex synthetic networks of nonlinear oscillators. We then employ our framework, along with a probabilistic model for heartbeat generation, to characterize the directed functional connectome of the human brain and to establish which parts of this connectome effect the directed central modulation of peripheral autonomic cardiovascular control. We demonstrate the effectiveness of our conditioning approach and unveil a top-down directed influence of the default mode network on the salience network, which in turn is seen to be the strongest modulator of directed autonomic cardiovascular control.