by the skin of your teeth

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Catching a train with literally ten seconds to spare.

Lo pillamos por los pelos.

'We caught it by the hairs' — por los pelos is the Spanish equivalent and it's perfect.

Context

Passing an exam with the minimum mark.

Aprobé raspando.

Raspar = to scrape — passed by scraping through. Vivid and very common.

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Arriving at a meeting just as it starts.

Llegué justo.

I arrived just in time — simple but effective. Add 'por los pelos' for drama.

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Finishing a project at the last possible second.

Lo entregué in extremis.

The Latin phrase 'in extremis' is used in Spanish too — at the last possible moment.

Context

Getting the last seat on a sold-out flight.

Me quedé con la última plaza por casualidad.

I got the last place by luck — coincidence and barely-there margins together.