Several riders slid and fell on wet and cobbled corners on the 32.4-km course, with defending champion Chloe Dygert ending up being the biggest casualty and having to settle for bronze.
Britain's Anna Henderson took second place, one minute 31.59 seconds behind Brown's winning time of 39 minutes 38.24.
Dygert hit the deck on a corner in the Bois de Vincennes, which effectively ended her chances of retaining her title and cost her second place as she ended 0.87 seconds behind Henderson.
For Brown, who is set to retire at the end of the year, the result was a mix of sheer joy and relief after she finished twice in second place at the road cycling world championships' time trial in 2022 and 2023.
There was disappointment for local favourite Juliette Labous, who took fourth place 9.20 seconds behind Dygert.
A day after heavy rainfall in the French capital, roads were damp all over the route, and several crashes occurred, with Denmark's Cecilie Uttrup Ludwig hitting the desk three times.
The event will be followed by the men's time trial, which will be raced over the same distance - a first in Olympic history.