Rangers' early dominance didn't last the half, though, after goalkeeper Jack Butland completely missed an inswinging corner, allowing George Stanger to stab in an equaliser from close range.
Butland's opposite number Beach almost had a horror moment of his own when his attempted clearance clattered off Cornelious and rebounded for Bojan Miovski to score, only for the effort to be ruled out for offside.
Kilmarnock's discipline and energy kept them in the match, even after Danilo nodded in off the post shortly after the break, but a second equaliser proved beyond them and Chermiti's fine hit put the result beyond doubt.
Frustration, then, for Stuart Kettlewell's visitors but a much-needed victory for Rohl as he tries to find his best side and formation.
It will take time but at least he's sent the Rangers faithful away savouring three points at home for the first time this term.