It should stay essentially in place even without substrate if you cover all four edges with poster hangers or report binders. It may tilt a bit, but if you cut it right it should be rigid enough to stand on its own.
Otherwise, burying the bottom section into the substrate should give it extra stability and stop fish from getting under the bottom. Using something heavy on both sides should also help to hold it up and stop it from leaning over.
I don't use store purchased dividers so not really familiar with available brands. Plus a lot of them tend to be clear, which can cause stress if housing two males side-by-side.