Responsible innovation, as a new management paradigm that balances the need for profit growth and the appeal of social value, plays an important role in taking into account corporate economic, social and environmental performance. It provides new ideas for driving enterprises to become more risk-resistant and sustainable in times of crisis. However, existing research on responsible innovation has mostly focused on content issues, and there is a lack of sufficient research and empirical studies on its effectiveness in business organizations. Based on the stakeholder theory and the research logic of “pressure–behavior-performance”, this study investigates the formation mechanism of responsible innovation and its impact on corporate performance. Through empirical research on 306 Chinese sample data, the results show that stakeholder pressure has a positive impact on corporate sustainability performance and responsible innovation plays a partially mediating role in this relationship. Flexible routine replication positively moderates the relationship between stakeholder pressure and responsible innovation, while positively moderating the mediating role that responsible innovation plays between stakeholder pressure and corporate sustainability performance. This study contributes to helping enterprises recognize the importance of responsible innovation in responding to stakeholder pressure and promoting corporate sustainability performance in times of crisis.