In experiments, subjects judged variations of sayings which did and did not rhyme, and tended to evaluate those that rhymed as more truthful (controlled for meaning). For example, the statement "What sobriety conceals, alcohol reveals" was judged to be more accurate than by different participants who saw "What sobriety conceals, alcohol unmasks".
The effect could be caused by the Keats heuristic, according to which a statement's truth is evaluated according to aesthetic qualities; or the fluency heuristic, according to which things could be preferred due their ease of cognitive processing.
For an example of the persuasive quality of the rhyme-as-reason effect, see "If it doesn't fit, you must acquit" the signature phrase used by Johnnie Cochran to gain acquittal for O.J. Simpson in Simpson's murder trial.