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Cardiac defibrillation is usually achieved using a single high-energy electric shock of up to 4,000 volts, which can be damaging to the heart tissue. Eberhard Bodenschatz and colleagues show how the disordered electrical dynamics that underlie cardiac fibrillation can be controlled using low-energy electrical pulses. They show, in tests on dogs, that intrinsic homogeneities in the cardiac tissue (such as the vasculature) serve as nucleation sites for the generation of waves of electrical activity that can target the instabilities and bring the tissue dynamics back into synchrony. The new technique, called low-energy antifibrillation pacing or LEAP, delivers five sequential low-energy electrical field pulses to the fibrillating heart — an average energy reduction of 84% compared to standard defibrillation. 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 substrate1,2,3,4. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation5,6,7. 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 ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ Eα. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show 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.