A degree of task completeness—a consequence of the division of labor and job specialization—might play an important role in employees’ motivation to be creative/innovative. While there is no consensus on whether having well-rounded or task-specialized work is optimal for employees’ innovative work behavior (IWB), we entertain the possibility that the preferred amount of this job attribute may condition individual reactions to a particular task structure. Moving beyond a traditional fit/misfit perspective of perceiving individuals as passive respondents, we expect that task-identity discrepancy (actual vs desired) triggers an employee to respond proactively by exhibiting job crafting, resulting in more frequent IWB. We test our hypotheses with mediated polynomial regression analyses based on a multi-source time-lagged field study of 184 professionals in a European bank and an experimental study with 81 students at an EU-based university. The results indicate that task-identity incongruence indirectly drives IWBs more than congruence. Specifically, both task-identity overfit (actual > desired) and task-identity underfit (desired > actual) are positively predicting IWB through job crafting as a coping mechanism for employees to adjust their work and unleash the innovative power from the experienced incongruence.