Savinova, the European woman Athlete of 2011, did not panic when defending champion Pamela Jelimo of Kenya kicked three metres clear down the back straight on the final lap.
Jelimo paid for going too soon and Savinova, 26, took over to storm to gold in one minute 56.19, with South African Caster Semenya producing a late burst to win silver in 1:57.23.
"It's just amazing. Right now I can't feel anything, but I'm amazed. It's been hard work, but it's the Olympics," said Savinova.
Semenya, the 2009 world champion whose emphatic victory in Berlin raised questions about her gender and started a verification process that still clouds her achievement, trailed the field at the bell and had too much ground to make up.
"I am happy with the result. I left it a bit late, but I am happy with the silver," said Semenya. "But my coach is not really happy."
As an unknown 18-year-old, Semenya emerged from obscurity to win the world title but her emphatic victory prompted the International Association of Athletics Federations to order an investigation into possible drug use and ask for a gender test.
The inquiry set off a long-running controversy, marked by media leaks, accusations and insults that enraged her home country and severely affected a shy girl from a rural village.
Semenya's sexuality became the subject of widespread debate and kept her off the track for almost a year before the IAAF cleared her to run again.
"I've been waiting all year for this. The last four years have not been easy," she said. "I'm already thinking about Rio (2016) and I hope I'll be there."
Semenya denied a suggestion from Colin Jackson that she tried not to win the race.
Former world champion Jackson told BBC viewers that he thought the South African was not concerned about winning gold because of the attention it may bring, claiming 'some athletes just want silver'.
Semenya seemed to be finishing strongly as Russia's Mariya Savinova took gold but started her charge for the line far too late, prompting Jackson to speculate on her motives.
"The plan was to win a gold but I made a wrong move," insisted Semenya.
"I'm happy with the silver medal but the main thing for an athlete is, of course, to win.
"I'm satisfied with silver, I'm still young and it's my first Olympics. I'll just have to train hard and maybe win a gold medal in the future but the really important thing was to finish on the podium.
"This is a good step forward for me and my coach, we will do better in the future."
Russian Ekaterina Poistogova clocked 1:57.53 for bronze. Jelimo faded out of the medals and was fourth.
"You have to accept that sometimes you are at the top and sometimes you are not," Jelimo said. "My body did not stick, but for me it's the best I can do."