It has recently been proposed that the evolution of human cooperativeness might, at least in part, have started as the cooptation of behavioral strategies evolved for solving problems of coordination to solve problems with higher incentives to defect, that is, problems of cooperation. Following this line of thought, we systematically tested human subjects for spillover effects from simple coordination tasks (2 × 2 stag hunt [SH] games) to problems of cooperation (2 × 2 prisoner’s dilemma [PD] games) in a laboratory experiment with rigorous controls to rule out subject confusion or habituation. Supporting the hypothesis that decision mechanisms for cooperation problems are linked with decision mechanisms for coordination, our main finding is that cooperation levels in PD games embedded in a sequence of SH games were significantly increased compared to a baseline sequence consisting only of PDs when subjects played in fixed pairs. No such effects could be found when players were randomly rematched each round. Additional findings include that this spillover effect cannot prevent a decay of cooperation over time, that there is no indication of a reversed effect (i.e., no signs of negative spillovers from failed cooperation to miscoordination), and that subjects’ self-reported preferences in SH games are prosocial.