Sustainable human exploitation of living marine resources stems from a delicate balance between yield stability and population persistence to achieve socioeconomic and conservation goals. But our imperfect knowledge of how oceanic oscillations regulate temporal variation in an exploited species can obscure the risk of missing management targets. We illustrate how applying a management policy to suppress fluctuations in fishery yield in variable environments (prey density and regional climate) can present unintended outcomes in harvested predators and the sustainability of harvesting. Using Atlantic cod (Gadus morhua, an apex predatory fish) in the Barents Sea as a case study we simulate age-structured population and harvest dynamics through time-varying, density-dependent and density-independent processes with a stochastic, process-based model informed by 27-year monitoring data. In this model, capelin (Mallotus villosus, a pelagic forage fish), a primary prey of cod, fluctuations modulate the strength of density-dependent regulation primarily through cannibalistic pressure on juvenile cod survival; sea temperature fluctuations modulate thermal regulation of cod feeding, growth, maturation, and reproduction. We first explore how capelin and temperature fluctuations filtered through cod intrinsic dynamics modify catch stability and then evaluate how management to suppress short-term variability in catch targets alters overharvest risk. Analyses revealed that suppressing year-to-year catch variability impedes management responses to adjust fishing pressure, which becomes progressively out of sync with variations in cod abundance. This asynchrony becomes amplified in fluctuating environments, magnifying the amplitudes of both fishing pressure and cod abundance and then intensifying the density-dependent regulation of juvenile survival through cannibalism. Although these transient dynamics theoretically give higher average catches, emergent, quasicyclic behaviors of the population would increase long-term yield variability and elevate overharvest risk. Management strategies that overlook the interplay of extrinsic (fishing and environment) and intrinsic (life history and demography) fluctuations thus can inadvertently destabilize fish stocks, thereby jeopardizing the sustainability of harvesting. These policy implications underscore the value of ecosystem approaches to designing management measures to sustainably harvest ecologically connected resources while achieving socioeconomic security.