A microscopic study of functional disorder-order folding transitions coupled to binding is performed for the p27 protein, which derives a kinetic advantage from the intrinsically disordered unbound form on binding with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) complex. Hierarchy of structural loss during p27 coupled unfolding and unbinding is simulated by using high-temperature Monte Carlo simulations initiated from the crystal structure of the tertiary complex. Subsequent determination of the transition-state ensemble and the proposed atomic picture of the folding mechanism coupled to binding provide a microscopic rationale that reconciles the initiation recruitment of p27 at the cyclin A docking site with the kinetic benefit for a disordered alpha-helix in the unbound form of p27. The emerging structural polarization in the ensemble of unfolding/unbinding trajectories and in the computationally determined transition-state ensemble is not determined by the intrinsic folding preferences of p27 but rather is attributed to the topological requirements of the native intermolecular interface to order beta-hairpin and beta-strand of p27 that could be critical for nucleating rapid folding transition coupled to binding. In agreement with the experimental data, the disorder-order folding transition for p27 is largely determined by the functional requirement to form a specific intermolecular interface that ultimately dictates the folding mechanism and overwhelms any local folding preferences for creating a stable alpha-helix in the p27 structure before overcoming the major free energy barrier.