Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate(1-4). In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation(5-7). Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density rho(E) and a characteristic time, tau, for tissue depolarization that obeys the power law tau proportional to E(alpha). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. Weshow in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.