The sensitive measurement of specific protein biomarkers is important for medical diagnostics and research. However, existing methods for quantifying proteins use antibody probes that cannot distinguish between specific and nonspecific binding, limiting their sensitivity and specificity. This work establishes a method for distinguishing between specific binding to the target protein and nonspecific binding to assay surfaces using single-molecule kinetic measurements with dynamically binding probes. This is significant because it permits extremely sensitive protein measurements without requiring a high-affinity detection antibody or any washing steps, enabling streamlined and sensitive quantification of proteins even when no pair of high-quality, tightly binding antibodies is available.