An expression to define that "very little span of time" [duplicate]

"Missed the plane by a whisker" would be one common such expression.

It is also used (and makes more intuitive sense) in non time related contexts such as a footballer missing the goal by a whisker.

by the skin of one's teeth is a common expression:

Fig. just barely. (By an amount equal to the thickness of the (imaginary) skin on one's teeth.

• I got through calculus class by the skin of my teeth.
• I got to the airport a few minutes late and missed the plane by the skin of my teeth.
• Lloyd escaped from the burning building by the skin of his teeth.

• Moment
  A brief, indefinite interval of time

• Instant
  An almost imperceptible space of time

• Twinkling of an eye

• In a flash
• Blink of an eye
• Split second

Examples,

• I was outbid of the ebay item within last moments of the auction.
• Cinderella transformed into a beautiful princess in the twinkling of an eye.

• 1 Corinthians 15:52 (various versions)
  in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed.

  It will happen in a moment, in the blink of an eye, when the last trumpet is blown. For when the trumpet sounds, those who have died will be raised to live forever. And we who are living will also be transformed.

  It will happen in an instant, in a split second at the sound of the last trumpet. Indeed, that trumpet will sound, and then the dead will come back to life. They will be changed so that they can live forever.