In early breast cancer progression, cancer cells invade through a nanoporous basement membrane (BM) as a first key step toward metastasis. This invasion is thought to be mediated by a combination of proteases, which biochemically degrade BM matrix, and physical forces, which mechanically open up holes in the matrix. To date, techniques that quantify cellular forces of BM invasion in 3D culture have been unavailable. Here, we developed cellular-force measurements for breast cancer cell invasion in 3D culture that combine multiple-particle tracking of force-induced BM-matrix displacements at the nanoscale, and magnetic microrheometry of localized matrix mechanics. We find that cancer-cell protrusions exert forces from picoNewtons up to nanoNewtons during invasion. Strikingly, the protrusions extension involves stepwise increases in force, in steps of 0.2 to 0.5 nN exerted from every 30 s to 6 min. Thus, this technique reveals previously unreported dynamics of force generation by invasive protrusions in cancer cells.