Sustainable use of common-pool resources is a major environmental governance challenge because of possible overexploitation. Communities devise self-governing institutions that avoid overuse and attain long-term benefits of cooperation. It is still unclear, however, what conditions allow cooperation to emerge, leading to greater long-term benefits. Until recently, studies of the sustainable governance of common-pool resources have overlooked feedback between user decisions and resource dynamics and failed to test the ability of shared goals to actually induce cooperation. Here we develop an online game to perform a set of experiments in which users of the same common-pool resource decide on their individual harvesting rates, which in turn are influenced by the resource dynamics. We show that if users share common goals, a high level of self-organized cooperation emerges, leading to long-term resource sustainability. Otherwise, selfish/individualistic behaviours lead to resource depletion. To explain these results, we develop a model of resource-decision dynamics based on optimal control theory and show how it is able to reproduce empirical results. We find that players self-organize and engage in collective action conducive to sustainable governance of common-pool resources by trade-off strategies that balance individual and collective payoff as well as short-term and long-term rewards.