Obtain voronoi polygons which extend till the boundary of another polygon

I think I may have a solution to your problem. Through the Sextante plugin you can access modules from a program called SAGA GIS. In the Points module is a tool called Thiessen Polygons. This is another name for Voronoi polygons. This tool should work for you. I just tried it out on a set of rain gauges and get the exact same coverage area that ArcGIS and grass (v.voronoi) give me. So I feel pretty confident in the output at least. I hope this helps.