Close Shave Loop Narrow Escape Driver Distracted Moment

1. The driver was distracted for just a moment and nearly hit another car. He missed the other car, but it was a close shave.
2. The spy had a close shave when she was nearly caught in the military camp. She had to climb a tree just to stay hidden.

The expression probably originates from the idea that a man who shaves closely is narrowly escaping cutting his skin.