The term 'win by a nose' is a phrase used to describe a situation in which one competitor or team narrowly beats another. The crossword solutions for this phrase are EDGE (4 letters) and EDGEOUT (7 letters). EDGE is a verb meaning to move slowly and gradually ahead of someone or something, while EDGEOUT is a verb meaning to gain an advantage over someone or something. Both words imply that the winner was only slightly ahead of the competition.