by a hair

Also,
by a hairbreadth or whisker
. Very narrowly. For example,
His serve was out by a hair
, or
We made our flight by a hairbreadth
, or
Dad missed hitting the pole by a whisker
. The first two hyperboles for the very narrowest margin date from the 1300s and 1400s respectively;
whisker
meaning “a small amount” was first recorded in 1913. Also see