Precis: In open-angle glaucoma, when neuroretinal rim tissue measured by volumetric optical coherence tomography (OCT) scans is below a third of the normal value, visual field (VF) damage becomes detectable. Purpose: To determine the amount of neuroretinal rim tissue thickness below which VF damage becomes detectable. Methods: In a retrospective cross-sectional study, 1 eye per subject (of 57 healthy and 100 open-angle glaucoma patients) at an academic institution had eye examinations, VF testing, spectral-domain OCT retinal nerve fiber layer (RNFL) thickness measurements, and optic nerve volumetric scans. Using custom algorithms, the minimum distance band (MDB) neuroretinal rim thickness was calculated from optic nerve scans. "Broken-stick" regression was performed for estimating both the MDB and RNFL thickness tipping-point thresholds, below which were associated with initial VF defects in the decibel scale. The slopes for the structure-function relationship above and below the thresholds were computed. Smoothing curves of the MDB and RNFL thickness covariates were evaluated to examine the consistency of the independently identified tipping-point pairs. Results: Plots of VF total deviation against MDB thickness revealed plateaus of VF total deviation unrelated to MDB thickness. Below the thresholds, VF total deviation decreased with MDB thickness, with the associated slopes significantly greater than those above the thresholds (P<0.014). Below 31% of global MDB thickness, and 36.8% and 43.6% of superior and inferior MDB thickness, VF damage becomes detectable. The MDB and RNFL tipping points were in good accordance with the correlation of the MDB and RNFL thickness covariates. Conclusions: When neuroretinal rim tissue, characterized by MDB thickness in OCT, is below a third of the normal value, VF damage in the decibel scale becomes detectable.