The late poet and novelist was awarded the major literary prize for her tenth and final collection Inside The Wave.
It includes the poem Hold Out Your Arms, which was written shortly before she died in June at the age of 64.
"An astonishing set of poems - a final, great achievement," Costa Book Award judges wrote.
Dunmore was among five authors awarded by the only major UK book prize open solely to authors living in the UK and Ireland.
Among her peers is the novelist Jon McGregor, who won the novel award for his fourth release Reservoir 13.
The judges called it "hypnotic, compelling and original" and said they were "simply blown away" by the book.
Reservoir 13 tells the story of a teenage girl who goes missing in the hills at the heart of England, and the group formed to search for her.
The first novel award went to Gail Honeyman, for her acclaimed debut Eleanor Oliphant Is Completely Fine, the story of a seemingly happy woman who is faced with change in her "carefully timetabled life".
The biography award was given to Rebecca Stott's memoir In The Days Of Rain, which left the judges "gripped and astonished by this unique life and the exquisite way she tells it".
The Explorer, by Katherine Rundell, picked up the children's book prize, although judges said the story could be of interest to everyone "aged eignt to 80".
The five winners, selected from 620 entries, will each receive £5,000.
One of the books will be chosen as the overall Costa Book of the Year, to be announced at a ceremony in London on 30 January.