We focus on dyadic interactions among supervisor- and employee-innovative work behavior (IWB) and how (in)congruence ([mis]fit) conditions relate to employee task performance. The logic of the person–supervisor (P–S) fit framework is used to explicate perceived supervisory performance ratings in the high-high fit and low-low fit situations, as well as designate the moderating effects of employee work engagement on the leader–member IWB incongruence–task performance link. A time-lagged two-source field research study on a sample of 157 employees and 40 direct supervisors from four public-sector organizations operating in an EU member state indicates that having highly innovative supervisors and likewise innovative employees produces the highest levels of employee task performance. Moreover, a moderated polynomial regression analysis revealed that employee work engagement buffers the effect of perceived misfit, elevating followers’ task performance in the condition of low supervisor-IWB and high employee-IWB. Contributions and implications for the innovation management and work engagement literature are discussed.