All replicating cells face an innate amount of replication stress. Stem cells, due to their role as progenitors, must also utilize efficient and high-fidelity pathways to minimize mutagenesis or delays in replication. Embryonic stem cells (ESCs) are rapidly proliferating stem cells isolated from an early embryo and have previously been shown to lack cell cycle checkpoints as well as accumulate much higher amounts of single-stranded (ssDNA) gaps. These gaps are thought to arise from PrimPol restarting stalled forks by repriming downstream from sites of damage, leaving ssDNA that must be filled in post-replicatively by translesion synthesis polymerases Polζ and Rev1. In this study, we utilized a flow cytometry assay that quantifies ssDNA accumulation by BrdU incorporation. Using this assay on cells treated with translesion synthesis (TLS) inhibitor JH-RE-06, we demonstrate the unique reliance of ESCs on TLS polymerase Polζ for ssDNA gap filling in G1 and S phases. Applying this assay revealed differential utilization of TLS in other cell types. Using immortalized mouse embryonic fibroblasts (MEFs), we demonstrate differentiation causes less reliance on TLS, implying reduced ssDNA stress and utilization of other pathways for repair. Through these experiments, we reveal another direction to understand DNA damage response pathways in vivo. We corroborate evidence that reliance on TLS is vital for ESCs. TLS is historically regarded as a low-fidelity pathway, but because ESCs have a much lower mutation rate, we propose that reliance on TLS, specifically Polζ-dependent repair, is in fact a high-fidelity response pathway that is essential for resolving ssDNA gaps.