Overtopping flows in landslide dams erode and entrain materials on the dam surface resulting in erosional features that undermine the dam stability and facilitate the subsequent outburst flooding. A comprehensive understanding of dam surface evolution is therefore crucial for flood risk assessment and hazard mitigation. In this research, we study the mechanisms that influence the non-uniform morphology evolution of landslide dam breaches (i.e., non-linear variation of the dam surface gradient) through experiments and numerical modeling. Analog landslide dam models, constructed using unconsolidated poorly sorted soils, are exposed to different inflow discharges. We find that although the breach discharge evolves more consistently with the erosion along the sidewalls than with bed erosion, it is the erosion along the bed that controls the change in dam surface profiles. Erosion rates, expressed as a function of the difference between the flow shear stress and the apparent erosion resistance, vary at different points along the dam surface due to localized erosional features induced by scouring. The apparent erosion resistance is found to increase linearly along the dam surface. Dam failure is numerically modeled using depth-averaged equations which assume that the complex evolution of the dam profiles is due to the coupled effects of erosion, entrainment, and channel bed collapse. Good agreement between the observed and modeled dam profiles further demonstrates that the gradual saturation of the breach flow with entrained sediment is responsible for the linear variation of the apparent erosion resistance, which in turn contributes to the formation of the surface scouring.