narrow escape - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
A barely successful flight from or avoidance of danger or trouble, as in He had a narrow escape, since the bullet came within inches of his head. This expression uses narrow in the sense of “barely sufficient.” [Late 1500s] For a newer synonym, see close call.