Passivating contacts are indispensable for achieving high conversion efficiency in crystalline-silicon solar cells. Their realization and integration into a convenient process flow have become crucial research objectives. Here, we report an alternative passivating contact that is formed in a single post-deposition annealing step called 'firing', an essential step for current solar cell manufacturing. As firing is a fast (<10 s) and high-temperature (>750 degrees C) anneal, the required microstructural and electrical properties of the passivating contact are stringent. We demonstrate that tuning the carbon content of boron-doped silicon-based thin films inhibits firing-induced layer delamination without preventing a partial crystallization. The latter promotes charge-carrier selectivity, even in the absence of a diffused doped region beyond the oxide, by inducing hole accumulation near the wafer surface. We fabricated proof-of-concept solar cells employing the developed technology, demonstrating an open circuit voltage of 698 mV and an efficiency of 21.9%, and show how it could be a drop-in replacement for today's rear contacts based on locally opened dielectric passivation stacks.