Biological macromolecules often exhibit correlations in fluctuations involving distinct domains. This study decodes their functional implications in RNA-protein recognition and target-specific binding. The target search of a peptide along RNA in a viral TAR-Tat complex is closely monitored using atomistic simulations, steered molecular dynamics simulations, free energy calculations, and a machine-learning-based clustering technique. An anticorrelated domain fluctuation is identified between the tetraloop and the bulge region in the apo form of TAR RNA that sets a hierarchy in the domain-specific fluctuations at each binding event and that directs the succeeding binding footsteps. Thus, at each binding footstep, the dynamic partner selects an RNA location for binding where it senses a higher fluctuation, which is conventionally reduced upon binding. This event stimulates an alternate domain fluctuation, which then dictates sequential binding footstep/s and thus the search progresses. Our cross-correlation maps show that the fluctuations relay from one domain to another specific domain until the anticorrelation between those interdomain fluctuations sustains. Artificial attenuation of that hierarchical domain fluctuation inhibits specific RNA binding. The binding is completed with the arrival of a few long-lived water molecules that mediate slightly distant RNA-protein sites and finally stabilize the overall complex. The study underscores the functional importance of naturally designed fluctuating RNA motifs (bulge, tetraloop) and their interplay in dictating the directionality of the search in a highly dynamic environment.