Overfishing to feed the world's growing population is depleting fish stocks. As these species are embedded in complex food webs, single-species management plans must be replaced with models integrating multispecies fisheries, economic market feedbacks, and fisher behaviour into complex ecological interaction networks to promote sustainable resource use. Here, we integrate three open-access fisheries in a dynamic model of complex food webs and find that selectively choosing similar species is more beneficial than harvesting species balanced across different network positions. Targeting low or high trophic levels risks reducing basal biomass or unchaining trophic cascades, respectively, undermining first ecological stability (biodiversity and biomass) and then economic sustainability (catch and revenue). A sustainable solution with high economic gain and low ecological impact arises when similar mid-trophic level species are caught. Our study demonstrates the importance of complex system analyses to balance ecological stability and multispecies fisheries to achieve a sustainable global food supply.