The shallowest regions of subduction megathrusts mainly deform aseismically, but they can sporadically host slow-slip events (SSEs) and tsunami earthquakes, thus representing a severe hazard. However, the mechanisms behind these remain enigmatic because the frictional properties of shallow subduction zones, usually rich in clay, do not allow earthquake slip according to standard friction theory. We present experimental data showing that clay-rich faults with bulk rate-strengthening behavior and null healing rate, typically associated with aseismic creep, can contemporaneously creep and nucleate SSE. Our experiments document slow ruptures occurring within thin shear zones, driven by structural and stress heterogeneities of the experimental faults. We propose that bulk rate-strengthening frictional behavior promotes long-term aseismic creep, whereas localized frictional shear allows slow rupture nucleation and quasi-dynamic propagation typical of rate-weakening behavior. Our results provide additional understanding of fault friction and illustrate the complex behavior of clay-rich faults, providing an alternative paradigm for interpretation of the spectrum of fault slip including SSEs and tsunami earthquakes.