knife-edge

A piece of steel sharpened to an acute edge or angle, and resting on a smooth surface, serving as the axis of motion of a pendulum, scale beam, or other piece required to oscillate with the least possible friction.

A precarious balance that could be upset by a very small force in either direction.

The game was on a knife-edge.

[…]meanwhile, Biloxi and Vincennes are both in the process of going down and being abandoned, whilst Miami is right on the knife-edge of being recoverable, with three destroyers clustering around offering pumping and additional damage-control crews to try and keep the light cruiser afloat.

Used other than figuratively or idiomatically: the edge of a knife.