In the middle of the night, I heard something break in the kitchen.

Literal

Night-middle [at-に] kitchen [in-で] thing [subj-が] breaks sound [subj-が] did.

物が壊れる is a relative clause modifying 音 — 'the sound of something breaking.' 音がする ('a sound is heard,' lit. 'a sound does') is the perception construction from the 声がする family. The overall structure: time + location + [relative clause]modifying sound + perception verb.