An analysis of gene expression variability can provide an insightful window into how regulatory control is distributed across the transcriptome. In a single cell analysis, the inter-cellular variability of gene expression measures the consistency of transcript copy numbers observed between cells in the same population. Application of these ideas to the study of early human embryonic development may reveal important insights into the transcriptional programs controlling this process, based on which components are most tightly regulated. Using a published single cell RNA-seq data set of human embryos collected at four-cell, eight-cell, morula and blastocyst stages, we identified genes with the most stable, invariant expression across all four developmental stages. Stably-expressed genes were found to be enriched for those sharing indispensable features, including essentiality, haploinsufficiency, and ubiquitous expression. The stable genes were less likely to be associated with loss-of-function variant genes or human recessive disease genes affected by a DNA copy number variant deletion, suggesting that stable genes have a functional impact on the regulation of some of the basic cellular processes. Genes with low expression variability at early stages of development are involved in regulation of DNA methylation, responses to hypoxia and telomerase activity, whereas by the blastocyst stage, low-variability genes are enriched for metabolic processes as well as telomerase signaling. Based on changes in expression variability, we identified a putative set of gene expression markers of morulae and blastocyst stages. Experimental validation of a blastocyst-expressed variability marker demonstrated that HDDC2 plays a role in the maintenance of pluripotency in human ES and iPS cells. Collectively our analyses identified new regulators involved in human embryonic development that would have otherwise been missed using methods that focus on assessment of the average expression levels; in doing so, we highlight the value of studying expression variability for single cell RNA-seq data.