Existing theoretical models of team innovation emphasize internal team processes and external conditions that facilitate or hinder innovation, but these models tend to be more suited for incremental than for radical innovation. Teams developing radical innovations face greater uncertainty and risk of failure and often encounter unanticipated challenges that require the concerted efforts of the team as a whole to move the project forward rather than face termination. Drawing on state goal orientation theory, we analyze the motivational drivers that position teams to effectively deal with such challenges. We propose a novel approach for managing team motivational states that involves adapting team goal preferences at key points in the innovation process in order to achieve radical innovation success. We advance a model highlighting teams' ability to dynamically shift shared goal orientations to meet acute “shocks” that disrupt regular team activities and threaten the survival of the innovation project. We identify the roles of ambidextrous leadership and reflexive team processes in achieving goal orientation shifts as important factors in radical innovation success. Although unanticipated challenges related to idea development and idea promotion may occur in both radical and incremental innovation projects, we argue that the effects are stronger the more radical the innovation.