Clincher (noun)

1. A final argument or piece of evidence that settles an issue or convinces someone of the truth of something.
2. A device used to fasten two parts together, especially in construction or mechanical applications.

Origin:

From the middle english word "clinchen" meaning "to fasten".

Examples:

1. The clincher in the debate was the speaker's use of statistics.
2. The clincher was the smoking gun that proved the defendant guilty.
3. The clincher in the argument was the eyewitness testimony.
4. The clincher was the nail in the coffin for the opposing team.
5. The clincher was the game-winning goal in the final minutes of the game.