Many embryonic organs undergo epithelial morphogenesis to form tree-like hierarchical structures. However, it remains unclear what drives the budding and branching of stratified epithelia, such as in the embryonic salivary gland and pancreas. Here, we performed live-organ imaging of mouse embryonic salivary glands at single-cell resolution to reveal that budding morphogenesis is driven by expansion and folding of a distinct epithelial surface cell sheet characterized by strong cell-matrix adhesions and weak cell-cell adhesions. Profiling of single-cell transcriptomes of this epithelium revealed spatial patterns of transcription underlying these cell adhesion differences. We then synthetically reconstituted budding morphogenesis by experimentally suppressing E-cadherin expression and inducing basement membrane formation in 3D spheroid cultures of engineered cells, which required β1-integrin-mediated cell-matrix adhesion for successful budding. Thus, stratified epithelial budding, the key first step of branching morphogenesis, is driven by an overall combination of strong cell-matrix adhesion and weak cell-cell adhesion by peripheral epithelial cells. Keywords: E-cadherin; branching morphogenesis; budding morphogenesis; cell-cell adhesion; cell-matrix adhesion; differential adhesion; epithelial morphogenesis; integrin; salivary gland; tissue engineering.