To establish the mechanism of unconventional superconductivity in Sr 2RuO4, a prerequisite is direct information concerning the momentum-space structure of the energy gaps Δi(k), and in particular whether the pairing strength is stronger ("dominant") on the quasi-one-dimensional (α and β) or on the quasi-two-dimensional (γ) Fermi surfaces. We present scanning tunneling microscopy measurements of the density of states spectra in the superconducting state of Sr 2RuO4 for 0.1Tc < T < Tc and analyze them along with published thermodynamic data using a simple phenomenological model. We show that our observation of a single superconducting gap scale with maximum value 2Δ≈5Tc along with a spectral shape indicative of line nodes is consistent, within a weak-coupling model, with magnetically mediated odd-parity superconductivity generated by dominant, near-nodal, Cooper pairing on the α and β bands. © 2013 American Physical Society.