While estimates of complex heartbeat dynamics have provided effective prognostic and diagnostic markers for a wide range of pathologies, brain correlates of complex cardiac measures in general and of complex sympatho-vagal dynamics in particular are still unknown. In this study we combine resting state functional Magnetic Resonance Imaging (fMRI) and physiological signal acquisition from 34 healthy subjects selected from the Human Connectome Project (HCP) repository with inhomogeneous point-process approximate and sample heartbeat entropy measures (ipApEn and ipSampEn) to investigate brain areas involved in complex cardiovascular control. Our results show that activity in the Temporal Gyrus, Frontal Orbital Cortex, Temporal Fusiform and Opercular cortices, Planum Temporale, and Paracingulate cortex are negatively correlated with ipApEn dynamics. Activity in the same cortical areas as well as in the Temporal Fusiform cortex are negatively correlated with ipSampEn dynamics. No significant positive correlations were found. These pioneering results suggest that cardiovascular complexity at rest is linked to a few specific cortical brain structures, including crucial areas connected with parasympathetic outflow. This corroborates the hypothesis of a multidimensional central network which controls nonlinear cardiac dynamics under a predominantly vagally-driven tone.