In their first starring vehicle, Fred Astaire and Ginger Rogers get shoved into conventional romantic-comedy roles, neither of which quite fit. He plays Guy Holden, a song and dance man who is otherwise your standard, persistent lothario. She plays Mimi Glossop, a young wife seeking a divorce, though mostly she’s defined by her ability to resist Guy’s advances. As Astaire and Rogers had already proven in Flying Down to Rio, where they had supporting parts as nimble smart-alecks commenting on the action, they were far cleverer than these rote roles. Still, it’s hard to argue with any vehicle that puts them behind the wheel. And so The Gay Divorcee rises above its framework, especially with its musical numbers. “The Continental” is an epic sequence that begins in Mimi’s hotel room and eventually sees the pair joining an intricately choreographed throng in the ballroom. “Let’s Knock Knees” is a comic tug of war between Betty Grable’s batting eyelashes and Edward Everett Horton’s elastic face. By far the highlight is Astaire and Rogers’ impossibly fluid routine to Cole Porter’s “Night and Day,” in which even that formidable song knows its place and quiets down for a portion of their dance. The two are so elegantly in sync that the ill-fitting conventions of The Gay Divorcee simply melt away.