There has been tremendous technological innovation in the healthcare sector, but it has also raised serious ethical and social concerns. The COVID-19 pandemic has only magnified these existing challenges. Hence, addressing these challenges becomes imperative in the “new normal.” In this context, this article uses a narrative synthesis approach to discuss the linkages of health technology, innovation, and policy to identify the challenges of this complex interaction by applying the principles of pragmatism and historicity to the existing literature. Moreover, the existing scientific mechanisms in the form of health technology assessment (HTA) and responsible innovation in health (RIH) are described to address these challenges. Using inductive epistemology, the linkages between HTA and RIH within a health innovation ecosystem framework are discussed for the future application of an integrated approach to address societal challenges. The proposed integrated approach of HTA and RIH is a work in progress and conceptualized as transdisciplinary, flexible, and adaptive, which is expected to facilitate future discussion, research, and policy action.