Fifty-five patients who were at high risk of relapse because of the size of the tumour were followed in the study published in Science Translational Medicine.
The scientists analysed the mutated DNA of the tumour and then continued to search the blood for those mutations.
Fifteen patients relapsed and the blood test gave advanced warning of 12 of them.
The other three patients all had cancers that had spread to the brain where the protective blood-brain barrier could have stopped the fragments of the cancer entering the bloodstream.
The test detected cancerous DNA in one patient who has not relapsed.