Based on the Spanish Technological Innovation Panel, this paper explores the role of R+D offshoring on innovation performance from 2004 to 2013. Specifically, we focus our attention on the impact of different types of offshoring governance models on the profitability of developing breakthrough innovations. Using a novel methodology for panel data sets, we control for the heterogeneity of firms as well as for the sample selection and endogeneity. Our study provides evidence that firms developing breakthrough innovations tend to benefit more from the external acquisition of knowledge than those engaged in incremental innovations. We also find evidence that acquiring knowledge from firms outside the group is more profitable than doing so with firms within the group. Moreover, the external acquisition of knowledge tends to present a higher return on breakthrough innovation in the case of taking such knowledge from the business sector rather than from universities or research institutions. Finally, the recent financial crisis has led to an increase in the return of the foreign acquisition of knowledge on the generation of breakthrough innovations.