By a narrow margin is an expression used when something or someone wins or loses by a small or slight difference. It's commonly used in politics, sports, and elections to describe a result that was decided by a few votes or a few points. However, there are other synonyms that you can use to replace this expression. Some of them include "by a whisker," "by a hair's breadth," "by a slim margin," "by the skin of one's teeth," "by a tiny fraction," and "by a small difference." These synonyms can add variety and depth to your writing, making it more engaging and interesting to your readers.