Cell migration during many fundamental biological processes including metastasis requires cells to traverse tissue with heterogeneous mechanical cues that direct migration as well as determine force and energy requirements for motility. However, the influence of discrete structural and mechanical cues on migration remains challenging to determine as they are often coupled. Here, we decouple the pro-invasive cues of collagen fiber alignment and tension to study their individual impact on migration. When presented with both cues, cells preferentially travel in the axis of tension against fiber alignment. Computational and experimental data show applying tension perpendicular to alignment increases potential energy stored within collagen fibers, lowering requirements for cell-induced matrix deformation and energy usage during migration compared to motility in the direction of fiber alignment. Energy minimization directs migration trajectory, and tension can facilitate migration against fiber alignment. These findings provide a conceptual understanding of bioenergetics during migration through a fibrous matrix.