The effect of financial resource constraints on innovation team performance is ambiguous. On the one hand, the majority of scholars have argued that financial resource constraints have an inhibiting effect on innovation, whereas budgetary slack supports creativity and innovation. Consistent with this notion, in most conceptual models on the management of innovation projects, the availability of slack, or at least adequate (rather than constrained) resources represents an important success factor supporting innovation. On the other hand, popular parlance has it that sometimes “necessity is the mother of innovation,” and literature in cognitive psychology suggests that resource constraints stimulate creativity and innovative behavior. Recent innovation literature indeed provides evidence that remarkable innovation outcomes can be achieved with constrained financial resources. Despite the rapidly growing research on success factors of innovation projects, and the high managerial relevance of budget questions, the influence of financial resource constraints has only very recently started to attract interest. The objective of the present study is to contribute to that research by investigating under what conditions financial resource constraints lead to innovation outcomes. Specifically, team climate for innovation is examined as a potentially important contingency variable of the relationship between financial resource constraints and innovation project performance. By explicitly focusing on team climate for innovation, factors of the work environment in innovation projects are addressed as influential boundary conditions for successfully innovating under financial resource constraints. The hypotheses are tested on a sample of 94 innovation project teams from a variety of industries. To ensure content validity and to avoid a possible common source bias, data from different respondents, i.e., team leaders, team members, and team external managers of the innovation projects, are used. Results of regression analyses show that there is no significant relationship between financial resource constraints and innovation project outcomes in terms of product quality and project efficiency. However, results show a significant interaction term of financial resource constraints and team climate for innovation in that team climate for innovation positively moderates the relationship between financial resource constraints and product quality as well as project efficiency. Thus, the findings of the present study contradict the widespread notion in innovation literature that financial resource constraints have a wholesale inhibiting effect on innovation, thereby providing a differentiated perspective on the relationship between financial resource constraints and innovation. On a practical level, the results of this study highlight a specific condition under which product developers can come up with more innovative solutions despite, or even because of, financial resource constraints.