Damage to which part of the brain would result in death due to the loss of heart function and blood pressure regulation?

The Answer is Medulla.

Explanation:

There are many parts of the brain which are responsible for the different functions.

Medulla is located in the brain stem in front of cerebellum. It is responsible for critical involuntary actions like breathing and heart rate. It control centers for heart and lungs.

Any damage to Medulla can result in death due to heart failure or blood pressure variation due to disturbed heart beat.