Hfq is a key regulator involved in multiple aspects of stress tolerance and virulence of bacteria. There has been an intriguing question as to how this RNA chaperone achieves two completely opposite functions--annealing and unwinding--for different RNA substrates. To address this question, we studied the Hfq-mediated interaction of fragments of a non-coding RNA, DsrA, with its mRNA target rpoS by using single-molecule fluorescence techniques. These experiments permitted us to observe the mechanistic steps of Hfq-mediated RNA annealing/unwinding at the single-molecule level, for the first time. Our real-time observations reveal that, even if the ring-shaped Hfq displays multiple binding sites for its interaction with RNA, the regulatory RNA and the mRNA compete for the same binding site. The competition makes the RNA-Hfq interaction dynamic and, surprisingly, increases the overall annealing efficiency by properly aligning the two RNAs. We furthermore reveal that when Hfq specifically binds to only one of the two RNAs, the unwinding process dominates over the annealing process, thus shedding a new light on the substrate selectivity for annealing or unwinding. Finally, our results demonstrate for the first time that a single Hfq hexamer is sufficient to facilitate sRNA-mRNA annealing.