One way is to trigger styled render intent using OpenLayers.Control.SelectFeature
Here is a demo which allows the line vertices (points) to become visible on hover.
UPDATE:
The key is to define a stylemap with two render intents, a default one, and another one for the hover style. Then set event listeners on the highlight control which will listen for the polygon, but trigger the highlight/unhighlight of the point.
HERE is a new DEMO that accomplishes what you want to do.

var polygonLayer = new OpenLayers.Layer.Vector("Polygons", {
styleMap: new OpenLayers.StyleMap({
"default": new OpenLayers.Style({
strokeColor: 'Transparent', // change this to strokeColor: '#0000cc', to see the polygons
fillColor: 'Transparent'
}),
"temporary": new OpenLayers.Style({
strokeColor: 'Transparent', // change this to strokeColor: '#0000cc', to see the polygons
fillColor: 'Transparent'
})
})
});
var pointLayer = new OpenLayers.Layer.Vector("Points", {
styleMap: new OpenLayers.StyleMap({
"default": new OpenLayers.Style({
strokeColor: 'Transparent',
fillColor: 'Transparent',
pointRadius: 6
}),
"temporary": new OpenLayers.Style({
strokeColor: '#0000cc',
fillColor: '#0000cc',
strokeOpacity: .8,
strokeWidth: 1,
fillOpacity: .3,
cursor: "default",
pointRadius: 6
})
})
});