Epidermal growth factor (EGF) receptor-mediated cell migration plays a vital role in invasion of many tumor types. EGF receptor ligands increase invasiveness in vivo, but it remains unclear how consequent effects on intrinsic cell motility behavior versus effects on extrinsic matrix properties integrate to result in net increase of translational speed and/or directional persistence of migration in a 3D environment. Understanding this convolution is important for therapeutic targeting of tumor invasion, as key regulatory pathways for intrinsic versus extrinsic effects may not be coincident. Accordingly, we have undertaken a quantitative single-cell imaging study of glioblastoma cell movement in 3D matrices and on 2D substrata across a range of collagen densities with systematic variation of protease-mediated matrix degradation. In 3D, EGF induced a mild increase in cell speed and a strong increase in directional persistence, the latter depending heavily on matrix density and EGF-stimulated protease activity. In contrast, in 2D, EGF induced a similarly mild increase in speed but conversely a decrease in directional persistence (both independent of protease activity). Thus, the EGF-enhanced 3D tumor cell migration results only partially from cell-intrinsic effects, with override of cell-intrinsic persistence decrease by protease-mediated cell-extrinsic reduction of matrix steric hindrance.