Mammalian embryogenesis commences with two pivotal and binary cell fate decisions that give rise to three essential lineages: the trophectoderm, the epiblast and the primitive endoderm. Although key signaling pathways and transcription factors that control these early embryonic decisions have been identified, the non-coding regulatory elements through which transcriptional regulators enact these fates remain understudied. Here, we characterize, at a genome-wide scale, enhancer activity and 3D connectivity in embryo-derived stem cell lines that represent each of the early developmental fates. We observe extensive enhancer remodeling and fine-scale 3D chromatin rewiring among the three lineages, which strongly associate with transcriptional changes, although distinct groups of genes are irresponsive to topological changes. In each lineage, a high degree of connectivity, or 'hubness', positively correlates with levels of gene expression and enriches for cell-type specific and essential genes. Genes within 3D hubs also show a significantly stronger probability of coregulation across lineages compared to genes in linear proximity or within the same contact domains. By incorporating 3D chromatin features, we build a predictive model for transcriptional regulation (3D-HiChAT) that outperforms models using only 1D promoter or proximal variables to predict levels and cell-type specificity of gene expression. Using 3D-HiChAT, we identify, in silico, candidate functional enhancers and hubs in each cell lineage, and with CRISPRi experiments, we validate several enhancers that control gene expression in their respective lineages. Our study identifies 3D regulatory hubs associated with the earliest mammalian lineages and describes their relationship to gene expression and cell identity, providing a framework to comprehensively understand lineage-specific transcriptional behaviors.