Nucleon quark wave functions deduced from deep-inelastic scattering are used to calculate baryon mass differences. The Hamiltonian used has a relativistic kinetic-energy operator and spin-dependent two-body oscillator potentials that break SU(6) strongly. With all parameters determined by deep-inelastic scattering fits, the Δ(1236)-N(939) mass difference is calculated in good agreement with experiment. The calculation is extended to the low-lying hyperons by introducing a strange-quark mass, fit to the Ω-. Using an SU(3)-breaking spin-spin force determined by the Λ0 magnetic moment (as suggested by quantum chromodynamics), good agreement is found for all low-lying baryon masses.