Based on fuzzy-set qualitative comparative analysis (fsQCA), this paper examines the interactions between the presence or absence of regional and national top-ranked research universities and other innovation-related conditions that foster regional competitiveness in the European Union context. We evaluated the effect of a region’s membership in different regional clusters as characterized by the following conditions: inter-firm collaboration in innovation activities, public R&D expenditure, private R&D expenditure as well as ranking in the list of the world’s top 300 (or top 100) universities. As one region might benefit from the presence of a local top-ranked university and/or from spillover effects from other national universities, we distinguish between the presence of universities within the region or elsewhere in the same country. Our results suggest that some conditions are necessary to achieve the outcome of being a “competitive region,” including having at least one top-300-ranked university in the same country (EU member state). Nevertheless, this attribute is not individually sufficient to incur the outcome of regional competitiveness. Our findings support the idea that the closeness of top-ranked universities does not itself guarantee regional competitiveness; instead, having an excellent research university within the same member state is only one of numerous configurations which may lead to a region’s success. These results support evidence in recent literature that leading research universities may be geographically connected to a wide network of actors with external knowledge interactions.