In a photo finish, Heath edged out Hungary's Kolos Csizmadia to secure his third consecutive medal at an Olympic Games in a time of 35.202 seconds.
The 36-year-old also set an Olympic-best time of 33.985 seconds in qualifying.
Following the race, Heath spoke to BBC Sport:
"I was maybe a bit hesitant off the start and didn't reach my potential in terms of peak speed.
"I am still happy with the performance. It is hard [another medal] to put into words. It is what you work towards to be at your best for these events."
Heath graduated in 2006 with a degree in Industrial Design and Technology and was awarded an Honorary Degree from the University in 2018.
Heath’s bronze is Loughborough’s tenth medal at the 2020 Tokyo Olympic Games, which includes three golds, five silvers, and two bronze medals.