Ortiz defeated Japan's Mika Sugimoto in a cagey, drawn-out final with little action, where both fighters struggled to get a grip or catch the other off balance.
The match went into overtime and judges eventually ruled Ortiz the winner.
Earlier in the day, Ortiz triumphed over the top-seeded Wen Tong of China in the semifinals.
Wen was the defending Olympic champion and was unbeaten at international competitions since 2007. She later won a bronze in the repechage. The other bronze medal was won by Britain's Karina Bryant.