Brown won Paralympic gold at Beijing 2008, the Commonwealth Games team title in Delhi two years ago and has now triumphed at London 2012.
Brown met compatriot Clarke - bronze medallist from Beijing - in the final, winning 6-4.
The Britons could not be separated early on, scoring 27-27 in the first set and 29-29 in the second, before three arrows of nine saw Brown, who was shooting first, take a 4-2 lead.
Clarke responded to take the fourth set 29-26 and level at 4-4 to force a fifth.
She required a maximum 10 score on the final arrow to win, but she shot a seven - her worst arrow of the final - as the pressure told and Brown won.
In the semi-finals, Brown claimed a 6-2 success over Marina Lyzhnikova and Clarke beat Stepanida Artakhinova, another Russian, 6-0.
Artakhinova claimed bronze with a 7-3 defeat of her team-mate Lyzhnikova.
Iran's Zahra Nemati won the women's Individual Recurve - W1/W2 gold medal with a 7-3 win over Elisabetta Mijno of Italy.
China's Li Jinzhi won bronze with a 6-4 defeat of Veronica Floreno of Italy.
In the women's Individual Recurve - Standing final, China's Yan Huilian claimed a 6-4 win over the Republic of Korea's Lee Hwa-sook.
Bronze was won by Milena Olszewska of Poland, who beat Mongolia's Javzmaa Byambasuren 6-2.