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Spatial refuges in peripheral habitats will become increasingly important for species persistence as climate change and other disturbances progressively impact habitat quality and assemblage compositions. However, the capacity for persistence will be determined in part by species‐specific abilities to absorb costs related to altered or decreased quantities and quality of resources at range peripheries.We compared variations in dietary strategies and energy acquisition trade‐offs along depth gradients in two obligate corallivores that differ in level of diet specialization. We also assessed depth‐related changes in energy pathways and energy content of their mixotrophic prey. We found no changes in feeding effort or total resource availability (total coral cover) towards deep range margins, but availability of the preferred resource (Acropora coral) decreased. While both species selectively targeted Acropora, the more specialized species (Chaetodon baronessa) exhibited limited feeding plasticity along the depth gradient. The degree of selectivity towards the preferred coral increased rather than decreased with depth, being 40 times greater than expected, given availability, at their range periphery. In contrast, the generalist's diet (Chaetodon octofasciatus) varied greatly in response to changes in resource availability with depth.Unexpectedly, the energy content of Acropora did not decline with depth, likely due to increased coral heterotrophy in deeper water, indicated by shifts in their molecular isotope geochemistry. This shift was accompanied by a 20% increase in plankton‐sourced carbon in the muscle tissue of deep‐resident fish, despite no observations of direct feeding on plankton food sources.Our results indicate that deep ranges in coral‐obligate reef fishes are supported by multiple mechanisms of trophic versatility in both the fish and corals. This nutritional plasticity likely serves a compensatory role in the resilience and eventual adaptation of organisms at their range peripheries.For species vulnerable to increasing anthropogenic impacts at range cores, variable and multi‐trophic functional responses can act to buffer against costs and increase the refuge potential of range peripheries. Specialist consumers may also be supported indirectly at range margins via trophic plasticity within their preferred prey. A free Plain Language Summary can be found within the Supporting Information of this article. [ABSTRACT FROM AUTHOR]