The Government is phasing out the scholarships this year and Ms Goulton and Mr Baillie are the last Otago University students to be awarded them.
Ms Goulton, based in the Otago pharmacology and toxicology department, will receive $104,460, and Mr Baillie, a physics student, will receive $99,816 during the three-year scholarships.
The ultimate aim is to use drugs to stimulate the brain's protective mechanisms in order to reduce the harm which could otherwise result from any subsequent stroke or other brain injury.
"I feel extremely lucky because it's such a good scholarship."
Mr Baillie said the scholarship provided "a great opportunity to be able to further my studies".
His PhD research involves the theory of ultra-cold gases, and work in this field could help improve understanding of how high-temperature superconductivity arises and how it might be enhanced.
Sixty-nine students have gained top achiever scholarships to study at Otago University since they were first awarded in 2002.
