The pronuncition of peace and piece is the only thing that these two words have in common.

piece: a portion or part of something, such as a pie or a cake; something regarded as a standard unit, such as a piece of paper or a piece of fruit.
Would you like a piece of pie?

peace: harmony and tranquility of environment, mind, politics or relationships. It often refers to a state of quiet, too.
He now has peace of mind

A good way to remember the difference is ‘a piece of pie’ because it has pie in it”.