Aisea Havili scored tries in each half to put the hosts on their way to a win in a dead-rubber Group D encounter.
James Brown also crossed, and kicked eight points, as the Dragons were limited to a converted Nic Fitisemanu try and a Ceri Sweeney penalty.
Worcester (7) 23
Tries: Havili (2), Brown
Pens: Brown (2)
Dragons (0) 10