Rivera passed out after posing for pictures and taking questions at a news conference after Sunday's show. She was given liquids and quickly recovered, said pageant spokeswoman Esther Swan.
Rivera, who was wearing a dress made entirely of metal chains, had been standing under hot stage lights for some time in the stifling auditorium when she began to topple over. Someone caught her as she fell.
Rivera, 18, won the title over 85 other contestants. Kurara Chibana of Japan was first runner-up; Lauriane Gillieron of Switzerland was second runner-up; and Lourdes Arevalos of Paraguay was third runner-up. Miss USA Tara Conner finished fourth.
A stunned Rivera covered her mouth with her hands as she was pronounced the winner. She beamed as last year's titleholder Natalie Glebova placed the crown on her brunette head.
"I always had faith and confidence in myself, but I never knew I was going to win," said Rivera, speaking in Spanish from the stage.
In her pageant biography, Rivera explained what made her different from the other contestants.
"Physically, I have been told by modeling agencies and friends that I represent the consummate Latino look," she said. "Everything in my face expresses our heritage, our music and the wonderful mixes of races that we are."
The 5-foot-9 Rivera is the first winner from Puerto Rico since Denise Quinones in 2001, and the fifth overall from the U.S. territory in the pageant's 55-year history.
In her spare time, Rivera said she likes watching the Latino version of "American Idol" and meditating. She hopes one day to act in U.S. and Latin American movies.
"My biggest goal in life is to become a great actress of infinite range," she said in her pageant biography. "I am a keen observer of the human behavior, which under my interpretation, is one of the best things an actress can do."
Conner was vying to become the first U.S. winner since Brook Lee in 1997. The Kentucky native wore a red-white-and-blue jockey outfit and cracked a whip during the opening parade of nations.
Several of the contestants sported costumes featuring colorful native dress, including feathers, sequins, fur, massive headpieces and, in the case of Miss Japan, a Samurai sword.
Lia Andrea Ramos of Philippines was chosen most photogenic in an online public vote. Angela Asare of Ghana won the congeniality award in a vote by all 86 contestants. Chibana, who carried the impressive looking Samurai sword, won the award for best national costume.
The winner travels the world for a year on behalf of charities and pageant sponsors. Rivera's prizes include a yearlong salary, a New York City apartment during her reign, and a modeling contract.
The celebrity judging panel included actor James Lesure of "Las Vegas"; "Desperate Housewives" creator Marc Cherry; actress Bridgette Wilson Sampras; former Dallas Cowboys star Emmitt Smith; and anchor Maria Celeste Arraras of Telemundo's "Al Rojo Vivo."