Ortiz, 22 and world number six, beat Japan's Mika Sugimoto in the final after she was awarded the win by the referee and two judges as the fight finished scoreless after extra time.
"I have no way to describe how I'm feeling right now," she told reporters. "I don't know whether to laugh or cry. All I can say is that I feel amazing right now."
Her route to gold in the +78kg category included a notable victory in the semi-final over China's Tong Wen, the reigning Olympic champion who had not lost an international fight since 2007.
"I've always said nobody's invincible. I've always thought that with anyone, not only Tong Wen, but anyone who competes against me," Ortiz said.
Cuba traditionally does well in judo, particularly in the women's categories, but had not won a gold since 2000 in Sydney.
"It was a challenge to keep up Cuba's results," she said. "For me, it means a lot (to do that)."
There was also a second medal in two days for Britain when outsider Karina Bryant, competing in her fourth Olympics, won bronze following a silver for Gemma Gibbons. That tally was the host nation's best judo haul since 1992.
Veteran Bryant, 33, put in a convincing display to beat Iryna Kindzerska of Ukraine to the delight of the crowd at London's ExCel Centre.
"It feels amazing. I'm over the moon, bit lost for words really. I've just kept believing in myself. I never doubted my potential," she told reporters.
"It was nice to share this experience with a British crowd."
China's Tong beat Brazil's Maria Suelen Altheman for the other bronze.
Chris Sherrington admitted he could have done better after his men's heavyweight campaign was ended by two-times world champion Alexander Mikhaylin.
Sherrington took just seconds to win his opening fight against Australia’s Jake Andrewartha, reducing him to tears with a brilliantly executed ippon, judo’s equivalent of a knockout blow.
But it was always going to be tougher against Russia’s Mikhaylin, a two-time world champion – although the last of those titles was seven years ago – who enjoyed a near perfect build-up to these Games.
He won bronze at last year’s World Championships, took the European title earlier this year and had only lost twice in 19 fights so far in 2012.
Sherrington – a serving Royal Marine – took the battle to the Russian and the contest stayed tight, with only a low-scoring move ending the British heavyweight’s hopes of a place in the quarter-finals.
“Nearly is not good enough, as a Royal Marine it needs to be a win for me to be totally happy,” he said.
“I’ve been trying to beat that guy for six years and I have worked and worked on him. But he manipulates you in ways you would not believe, you can’t see it, you have to feel it.
“I managed to keep him at bay right until the end and I’m gutted but at the end of the day I got taken out by a two-time world champion.
“That’s the closet I’ve ever got to him. I’m in the best shape I’ve ever been in, I’m fast and strong and powerful but he still won.
“It was a low score, it wasn’t an ippon and maybe next time he will get what’s coming.”
- Tong Wen