What is the lowest part of the brain that controls breathing and heart beat?

Medulla is the lowest part of the brain that controls breathing and heart beat.

The brain stem is  located beneath the limbic system. It is responsible for another vital life function like breathing, heartbeat, and blood pressure. It is made up of the midbrain, pons, and medulla.

The primary role of PONS is to serve as a bridge between various parts of the nervous system, including the cerebellum and cerebrum.

The primary role of MEDULLA is regulating our involuntary life sustaining functions such as breathing, swallowing, and heart rate. As part of the brainstem, it also helps transfer neural messages to and from the brain and the spinal cord. It is located at the junction of the spinal cord and the brain.