Global warming triggers permafrost thaw, which increases the release of terrigenous organic matter (terr-OM) to the Arctic Ocean by coastal erosion and rivers. Terrigenous OM degradation in the Arctic Ocean contributes to greenhouse gas emissions and severe ocean acidification, yet the vulnerability of different terr-OM components is poorly resolved. Here, terr-OM degradation dynamics are studied with unprecedented spatial coverage over the World's largest shelf sea system-the East Siberian Arctic Shelf (ESAS), using a multi-proxy molecular biomarker approach. Mineral-surface-area-normalized concentrations of terr-OM compounds in surface sediments decreases offshore. Differences between terr-OM compound classes (lignin phenols, high-molecular weight [HMW] n-alkanes, n-alkanoic acids and n-alkanols, sterols, 3,5-dihydroxybenzoic acids, cutin acids) reflect contrasting influence of sources, propensity to microbial degradation and association with sedimenting particles, with lignin phenols disappearing 3-times faster than total terr-OM, and twice faster than other biomarkers. Molecular degradation proxies support substantial terr-OM degradation across the ESAS, with clearest trends shown by: 3,5-dihydroxybenzoic acid/vanillyl phenol ratios, acid-to-aldehyde ratios of syringyl and vanillyl phenols, Carbon Preference Indices of HMW n-alkyl compounds and sitostanol/β-sitosterol. The combination of terr-OM biomarker data with δ¹³C/Δ¹⁴C-based source apportionment indicates that the more degraded state of lignin is influenced by the relative contribution of river-transported terr-OM from surface soils, while HMW n-alkanoic acids and stigmasterol are influenced by erosion-derived terr-OM from Ice Complex deposits. Our findings demonstrate differences in vulnerability to degradation between contrasting terr-OM pools, and underscore the need to consider molecular properties for understanding and modeling of large-scale biogeochemical processes of the permafrost carbon-climate feedback.