Scholars have long been intrigued by the relationship between intrateam conflict and team creativity, though findings to date have been mixed. Recent research suggests that traditional conceptualizations of intrateam conflict as a property that is shared uniformly by team members (e.g., averaging members' overall conflict perceptions), rather than a more nuanced phenomenon between individual members with unique network positions, have limited our understanding of its influences. These advances, however, have yet to be substantively applied to the intrateam conflict‐creativity literature. Accordingly, we integrate network views of conflict with creativity theory and group motivated processing models to explore how task and relationship conflicts involving critical members' (i.e., members central to a team's workflow network) influence team creative functioning beyond overall conflict perceptions. We theorize that critical member task conflict is positively associated with team creativity by way of team reflexivity, and this positive indirect effect is accentuated by team shared goals. Further, we posit that critical member relationship conflict is negatively associated with team creativity by way of reduced team cohesion, though this effect is mitigated by critical member emotional intelligence. Analyses of 70 new product development teams support most hypotheses while also highlighting interesting nuance and future research opportunities.