The German rider added the individual title to the team title she won on Sunday as she beat Ukraine's Anna Solovey on the 29.5-kilometre course.
Going out as rider number 47 of 49, Brennauer overcame poor weather conditions on Tuesday to finish in a time of 38 minutes 48.16seconds, clinching gold by 18.68secs.
United States' Evelyn Stevens claimed bronze, but defending champion Ellen van Dijk was never in contention and had to settle for seventh.
The race began in earnest when Germany's Mieke Kroeger went fastest as Van Dijk, the final competitor, took to the course.
Kroeger's lead did not last long, though, as Solovey turned a high gear and began to pick up time on her rivals.
Van Dijk looked set to compete, but the Dutchwoman was 17secs off the pace by the second time check and seemingly out of the running.
Solovey crossed the line nearly 20secs quicker than Kroeger after two very quick sections to leave her on the verge of the title.
However, Brennauer was not finished, although she had to produce a stunning final sector to take gold.
Stevens was in contention during her ride, but was only able to slot into third position, while Linda Villumsen (New Zealand) and Van Dijk were hampered by a downpour of rain.
Both struggled to maintain their pace in the changing conditions to end any hope they had of making the top three.