Won by a hair 的意思是以毫厘之差取得险胜、以微弱优势取胜。头发丝常用来比喻微小的事物，仅以微弱优势取胜，自然也就是险胜了。

【例句】
She only won by a hair but that still makes her our new governor.
她以微弱的优势赢得胜利，当上了州长。

We won by a hair's breadth.
我们以些微之差赢了对手。