Summary Genes with expression levels that fluctuate on timescales longer than cell division times are associated with cancer drug tolerance. However, current methods for identifying such “memory” genes rely on variants of the Luria-Delbrück experiment and require either multiple replicates or lineage information, constraints that limit their use to model systems or in vitro settings. We develop a conceptual approach using recent results in random matrix theory to demonstrate that the existence of memory genes results in a power-law signature in the cell covariance matrix eigenspectrum. Utilizing this theoretical framework, we develop Power-Seek, an algorithm to discover memory genes from a single-time-point, single-cell RNA sequencing (scRNA-seq) dataset. Without using prior information on lineages or cell-cycle times, Power-Seek correctly identifies memory genes in a melanoma cell line. Our results open up the possibility of identifying expression states driving drug tolerance in real-world scenarios, as we demonstrate using data from a human breast cancer tissue sample. A record of this paper’s transparent peer review process is included in the supplemental information.