Thin-film photovoltaics offers a path to significantly decarbonize our energy production. Unfortunately, current materials commercialized or under development as thin-film solar cell absorbers are far from optimal as they show either low power conversion efficiency or issues with earth-abundance and stability. Entirely new and disruptive materials platforms are rarely discovered as the search for new solar absorbers is traditionally slow and serendipitous. Here, we use first principles high-throughput screening to accelerate this process. We identify new solar absorbers among known inorganic compounds using considerations on band gap, carrier transport, optical absorption but also on intrinsic defects which can strongly limit the carrier lifetime and ultimately the solar cell efficiency. Screening about 40,000 materials, we discover the Zintl-phosphide BaCd$_{2}$P$_{2}$ as a potential high-efficiency solar absorber. Follow-up experimental work confirms the predicted promises of BaCd$_{2}$P$_{2}$ highlighting an optimal band gap for visible absorption, bright photoluminescence, and long carrier lifetime of up to 30 ns even for unoptimized powder samples. Importantly, BaCd$_{2}$P$_{2}$ does not contain any critical elements and is highly stable in air and water. Our work opens an avenue for a new family of stable, earth-abundant, high-performance Zintl-based solar absorbers. It also demonstrates how recent advances in first principles computation can accelerate the search of photovoltaic materials by combining high-throughput screening with experiment.