Accurate EF1Σg+-X1Σg+ transition energies in molecular hydrogen were determined for transitions originating from levels with highly excited vibrational quantum number, v = 11, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H2∗, produced via the photodissociation of H2S, yielding transition frequencies with accuracies of 45 MHz or 0.0015 cm−1. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing 7 pπ electronic Rydberg states, resulting in narrow transitions due to reduced ac-Stark effects. Using known EF level energies, the level energies of X(v = 11, J = 1, 3–5) states are derived with accuracies of typically 0.002 cm−1. These experimental values are in excellent agreement with and are more accurate than the results obtained from the most advanced ab initio molecular theory calculations including relativistic and QED contributions.