Analyzing the impact of a sustainability agenda in research and innovation on system transition is a critical research topic. This literature stream aims to examine how research and innovation can deal with wicked-problems at a dynamic system level to create more sustainable future systems. However, this study addresses two main issues in the current sustainability transition literature. First, the literature to date offers little insight into concrete implications for the management of innovation processes at the organizational level. Second, sustainability is often addressed as per se desirable. While the concept of Sustainable Innovation (SI) can valuably contribute in addressing the first issue by providing essential features to analyze business management procedures and their broader implications on socio-technical systems, it falls short in addressing the second issue. Essential aspects of sustainability, such as the responsibility for potential future trade-offs through innovation, are not strategically integrated into the current framework. This study argues that without strategic integration of responsibility, there is a risk of contributing to a partially-sustainable—”irresponsible”—socio-technical system change as a result of business innovation activities. Therefore, an extended innovation process model for sustainability to embed responsibility at the core of innovation activities is required. For this purpose, the framework of Responsible Research and Innovation (RRI) is utilized. This paper reports on findings from a systematic literature review of a representative sample of empirical studies from the SI and RRI literature. Thereby, the goal was to extend the understanding of management opportunities within innovation processes for sustainability through the implementation of RRI principles, in order to create sustainable socio-technical systems.