The Fontan operation is a palliative surgical procedure performed on children, born with congenital heart defects that have yielded only a single functioning ventricle. The total cavo-pulmonary connection (TCPC) is a common variant of the Fontan procedure, where the superior vena cava (SVC) and inferior vena cava (IVC) are routed directly into the pulmonary arteries (PA). Due to the limited pumping energy available, optimized hemodynamics, in turn, minimized power loss, inside the TCPC pathway is required for the best optimal surgical outcomes. To complement ongoing efforts to optimize the anatomical geometric design of the surgical Fontan templates, here, we focused on the characterization of power loss changes due to the temporal variations in between SVC and IVC flow waveforms. An experimentally validated pulsatile computational fluid dynamics solver is used to quantify the effect of phase-shift between SVC and IVC inflow waveforms and amplitudes on internal energy dissipation. The unsteady hemodynamics of two standard idealized TCPC geometries are presented, incorporating patient-specific real-time PC-MRI flow waveforms of “functional” Fontan patients. The effects of respiration and pulsatility on the internal energy dissipation of the TCPC pathway are analyzed. Optimization of phase-shift between caval flows is shown to lead to lower energy dissipation up to 30% in these idealized models. For physiological patient-specific caval waveforms, the power loss is reduced significantly (up to 11%) by the optimization of all three major harmonics at the same mean pathway flow (3 L/min). Thus, the hemodynamic efficiency of single ventricle circuits is influenced strongly by the caval flow waveform quality, which is regulated through respiratory dependent physiological pathways. The proposed patient-specific waveform optimization protocol may potentially inspire new therapeutic applications to aid postoperative hemodynamics and improve the well being of the Fontan patients.