Simultaneously achieving high voltage and high efficiency in thin-film solar cells is of paramount importance for real-world applications. While solar cells fabricated from the Earth-abundant kesterite absorber Cu2ZnSn(SxSe1−x)4 provide an attractive, non-toxic, energy harvesting solution, their utilization has been constrained by relatively low open-circuit voltages that limit efficiency. Increasing the sulfur content to widen the bandgap boosts the voltage, but usually at the expense of efficiency. Here, we report important progress on this fundamental problem by fabricating solar cells with high sulfur content that exhibit efficiencies up to 11.89% with open-circuit voltages as high as 670 mV. In a multistep process, fully functional solar cells are separated from their growth substrate, and a high-work-function back contact is subsequently deposited. With this approach, we fabricated a series-connected device that produces 5.7 V under 1 Sun illumination and ~2 V under low lighting conditions, below 10−3 Suns.