It took tremendous courage for Gabby Douglas to move away from home at 14, leaving her beloved mother and siblings behind in Virginia Beach, to train with a world-class coach who would push her to excel.

And it took untold practice, sacrifice and pain for Douglas and Liang Chow to transform this better-than-average gymnast with bigger-than-average dreams into a bona-fide Olympian in less than two years’ time.

Thursday at the London Games, Douglas demonstrated that the world likely hasn’t seen the limit of what this uncommonly self-possessed youngster can do by winning the sport’s most prestigious title: the individual all-around Olympic gold medal.

Douglas seized the lead at the outset with the world’s most difficult vault and then stood tall, at 4 feet 11, to fend off a charge by two formidable Russians, delivering a performance that was packed with power, grace and a palpable joy that women’s gymnastics sorely lacks.

“You just have to not be afraid and go out there and just dominate,” Douglas said afterward, a stuffed Olympic mascot under one arm, a bouquet of flowers in one hand and an Olympic gold medal around her neck. “You have to go out there and be a beast. Because if you don’t, you’re not going to be on the top.”

Douglas, who finished with 62.232 points, became the third consecutive American woman to win the coveted individual all-around gold, following Nastia Liukin, the 2008 Beijing champion, and Carly Patterson, who triumphed at the 2004 Athens Games.

She’s also the first African-American to win the all-around title. It was Douglas’s second gold medal in 48 hours, coming on the heels of the U.S. women’s team championship Tuesday.

Russia’s Viktoria Komova, an elegant gymnast who had been chasing Douglas all night, took silver, breaking down in uncontrollable sobs when the scoreboard showed that her final routine, an inspired performance on the floor, wasn’t enough to vault her into gold. Komova finished with 61.973.

American Aly Raisman, 18, a surprising qualifier for Thursday’s final, earned the same score as Russia’s Aliya Mustafina (59.566), leaving them tied them for the bronze medal. But under the sport’s international code, such ties are broken by a rule that neither Raisman nor her coach, Mihai Brestyan, was aware of.

In short: the lowest score of each gymnast is dropped, then the remaining three scores are added together to settle it. After that calculation, Mustafina held the edge, with 45.933 to Raisman’s 45.366.

Raisman was given no official explanation and walked off the floor still hopeful of a shared bronze. A journalist broke the news.

“I was hoping that they’d given us both the bronze medal, but obviously they didn’t,” said Raisman, of Needham, Mass., who had outperformed her best friend and teammate Jordyn Wieber to earn the unexpected chance to contend for the individual title. “It’s definitely upsetting, but I’m still happy for the rest of the girls that are on the podium tonight.”

Raisman still has a chance to win two more medals, having qualified for the finals on the balance beam and floor. Douglas could also add to her London medal haul, as well, when the individual event finals are held.

But not all of Douglas’s Olympic ambitions dangle from purple satin ribbons.

“I hope I inspire people,” said Douglas, breaking out into an enormous smile. “I want to inspire people!”

And her message?

“If you’re having a hard time, never give up! Always keep fighting!”

Even at 16 years old, Douglas speaks from experience. She has dealt with injuries — missing the 2009 national championships because of a broken wrist and struggling with a strained hip flexor and hamstring in 2010. And two years ago, she made the wrenching decision to leave her close-knit family to live with a foster family in West Des Moines, Iowa, and train with Chow at the same gym as 2008 all-around silver medalist Shawn Johnson.

Thursday at North Greenwich Arena, the 94-pound Douglas took the fight directly to her 23 challengers.

She opened with the high-risk Amanar vault, which just a handful of gymnasts in the world perform. It automatically adds 0.7 of a point to a gymnast’s score because of its difficulty, but that gain can be quickly negated by botched execution or a muffed landing.

Douglas was flawless on the handspring takeoff and through 21 / 2 twists in the air, but she wobbled slightly upon the landing. Still, her score, 15.966, was the highest among all 24 vault performances.

Raisman’s was nearly as good, 15.900, putting the Americans 1-2 after the first rotation.

Then came the uneven bars, a strength of the Russians and mixed bag for the Americans. And the lithe Komova demonstrated why she’s the reigning world champion on the apparatus. Her reedlike body is ideally suited for whipping around the uneven bars, and she did so with effortless grace, her legs perfectly aligned. Mustafina was more daring, and stylish as well.

Douglas her held her own, while Raisman fell to fourth behind the Russia duo.

Whatever nerves a gymnast feels tend to show themselves on the balance beam. Douglas, whose ability to focus throughout a competition was in question earlier in the season, held hers together impressively, somersaulting up and down the four-inch-wide beam as if it were wide as a sidewalk and quickly composing herself after each slight wobble.

But beam was disastrous for the normally solid Raisman. She never fell off but was penalized a full point, as costly as if she had fallen, for using a hand to keep herself from tumbling off.

Raisman’s coach was baffled afterward, having watched her nail the routine in the U.S. team qualifying earlier in the week and twice in warmups that morning,

“When it’s about the team, she is giving everything,” Brestyan said. “When it’s about herself, something is wrong there. I don’t know why. It’s a shame.”

Douglas had a comfortable leading entering the final event, the floor, but not so comfortable that she could relax. Chow had forbid her from looking at the scoreboard throughout the competition, telling her to focus solely on him and the apparatus.

She peeked anyway, she confessed afterward.

But that hardly kept her from staging a full-tilt show. She brought the house down with a high-energy, fun-loving routine that mixed explosive athleticism with sassy dance moves. Her jumps were spectacular; her tumbling, daring but always in control. Her score, 15.359, put tremendous pressure on Komova, the only gymnast in position to overtake.

And in the end, Douglas’s mark stood. And she disappeared from view in a sea of hugs.

“She performs with extreme lightness,” said U.S. team coordinator Marta Karolyi, who dubbed Douglas “The Flying Squirrel” after first seeing her perform two years ago. “I think that was one of the qualities that the international judges appreciated. She wasn’t struggling. She wasn’t just barely pulling through the skills. She was really flying the air, like her name says!”