The former Rangi Ruru Girls School student rowed alongside fellow Kiwi, Alice White, to beat Oxford University by more than 11 boat lengths on Monday morning (NZ time).
The Cambridge crew also set a new course record of 18 minutes 33 seconds.
Dawson's parents, John and Kathy, and brother Sam all travelled to London for the race.
Kathy said she is very proud of Anna's achievements because she has had to overcome much adversity recently.
18 months ago Anna was forced to return to New Zealand from the States, where she'd been studying at Stanford University on scholarship for 5 years, as she was unable obtain a US work visa.
"We thought she’d be devastated when she returned home, however when she arrived I remember her saying ‘I have to get my life in order’ and then set about working hard to create opportunities for herself." Kathy said.
The annual race has been running since 1845 and is one of the oldest sporting rivalries in the world.