Rumford finished at 14-under-par 274 for his second career triumph on the European Tour.
Peter Lonard, the veteran Australian whose quest for a first European Tour title continues, was one shot further back at nine-under-par 279.
Rumford earned his playing status on the European Tour with a win at last year's Aa St. Omer Open.
Rumford trailed Lonard by a stroke to start the final round. But, while Lonard parred each of his first four holes, Rumford birdied three in a row starting at the second to take the lead at 12-under.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys