DEAD-box helicase proteins accelerate folding and rearrangements of highly structured RNAs and RNA-protein complexes (RNPs) in many essential cellular processes. Although DEAD-box proteins have been shown to use ATP to unwind short RNA helices, it is not known how they disrupt RNA tertiary structure. Here, we use single molecule fluorescence to show that the DEAD-box protein CYT-19 disrupts tertiary structure in a group I intron using a helix capture mechanism. CYT-19 binds to a helix within the structured RNA only after the helix spontaneously loses its tertiary contacts, and then CYT-19 uses ATP to unwind the helix, liberating the product strands. Ded1, a multifunctional yeast DEAD-box protein, gives analogous results with small but reproducible differences that may reflect its in vivo roles. The requirement for spontaneous dynamics likely targets DEAD-box proteins toward less stable RNA structures, which are likely to experience greater dynamic fluctuations, and provides a satisfying explanation for previous correlations between RNA stability and CYT-19 unfolding efficiency. Biologically, the ability to sense RNA stability probably biases DEAD-box proteins to act preferentially on less stable misfolded structures and thereby to promote native folding while minimizing spurious interactions with stable, natively folded RNAs. In addition, this straightforward mechanism for RNA remodeling does not require any specific structural environment of the helicase core and is likely to be relevant for DEAD-box proteins that promote RNA rearrangements of RNP complexes including the spliceosome and ribosome.