Examples:

He slipped at the edge of the cliff but managed to hold on to a rock, and was saved by the skin of his teeth.

However, when you have just avoided relegation by the skin of your teeth, treading water is not an option.

After being chased by the police a long way, the criminal managed to escape by the skin of his teeth.

You're thrown in at the deep end, barely prepared for such warfare and surviving by the skin of your teeth.

The team held on by the skin of their teeth to win the crucial match. Source: theidioms.com