Gradients of diffusive molecules within 3D extracellular matrix (ECM) are essential in guiding many processes such as development, angiogenesis, and cancer. The spatial distribution of factors that guide these processes is complex, dictated by the distribution and architecture of vasculature and presence of surrounding cells, which can serve as sources or sinks of factors. To generate temporally and spatially defined soluble gradients within a 3D cell culture environment, we developed an approach to patterning microfluidically ported microchannels that pass through a 3D ECM. Micromolded networks of sacrificial conduits ensconced within an ECM gel precursor solution are dissolved following ECM gelation to yield functional microfluidic channels. The dimensions and spatial layout of channels are readily dictated using photolithographic methods, and channels are connected to external flow via a gasket that also serves to house the 3D ECM. We demonstrated sustained spatial patterning of diffusive gradients dependent on the architecture of the microfluidic network, as well as the ability to independently populate cells in either the channels or surrounding ECM, enabling the study of 3D morphogenetic processes. To highlight the utility of this approach, we generated model vascular networks by lining the channels with endothelial cells and examined how channel architecture, through its effects on diffusion patterns, can guide the location and morphology of endothelial sprouting from the channels. We show that locations of strongest gradients define positions of angiogenic sprouting, suggesting a mechanism by which angiogenesis is regulated in vivo and a potential means to spatially defining vasculature in tissue engineering applications. This flexible 3D microfluidic approach should have utility in modeling simple tissues and will aid in the screening and identification of soluble factor conditions that drive morphogenetic events such as angiogenesis.