Boudia's victory by 1.08 points over Qiu Bo of China gave the U.S. its first gold in diving since 2000, and was the first by an American man since the late Mark Lenzi won the 3-meter springboard at the 1992 Barcelona Games.
"Oh, my God, I don't have words for it," said Greg Louganis, the diving great who swept the springboard and platform events at the 1984 and 1988 Olympics and who has mentored Boudia.
On the medals stand, Boudia wiped his brow as if to say, "Whew!"
It was that close.
The American scored 568.65 points in the six-dive final. Qiu took the silver at 566.85.
Tom Daley of Britain settled for the bronze at 556.95 after leading going into the final dive in front of a raucous home crowd that included David Beckham and his three sons.
"Tom Daley dove the lights out, Qiu Bo dove the lights out," Boudia said. "I only did what I do in practice."
Daley scored 90.75 on his last dive, including one 10, but Boudia and Qiu each did the same tougher dive in the last round.
Boudia, tied for second with Qiu going into the last round, scored 102.60 points on a back 2 1/2 somersault with 2 1/2 twists pike worth a 3.6 degree of difficulty. It was the highest score of any dive in the final.
Qiu followed him and scored 100.80, not quite enough to deliver a seventh gold for China in these games.
"I was very nervous," Qiu said through a translator. "I have competed so many times but I have never had that much nervousness."
China won six golds, first losing the men's 3-meter springboard to spoil its bid for a sweep of the eight gold medals, and then coming up short in the last diving event at the London Games.
Qiu rested his head against the wall behind the diving boards in anguish.
"It is OK," the 19-year-old diver said. "I am still young and I will be back."
Boudia, meanwhile, shared in a group hug with his coaches and teammates, a broad smile on his face.
"I dreamed about this," Boudia said. "It didn't even feel like I was diving it was so surreal."
The 23-year-old diver from Noblesville, Ind., came out to find his family and friends after the medals ceremony. Boudia climbed into the stands to share hugs and kisses with his supporters who wore royal blue T-shirts with "Boudia" on the back.
Nick McCrory, the other American, finished ninth in his first Olympics.
"I knew he could do it," he said, referring to Boudia. "He was ending with a solid dive and he hit it. I'm so happy for him. He really earned it."
Boudia's victory was the fourth diving medal won by the U.S. in London after the Americans were shut out at the previous two Olympics for the first time. They won a silver and two bronze medals in the synchro events. It was the first U.S. diving gold since Laura Wilkinson upset the Chinese on women's platform at the Sydney Games.
"We're headed in the right direction," Louganis said.
Daley was in contention until the very end to try to win the host country's first Olympic diving gold. But he appeared plenty happy with his bronze medal, jumping into the diving pool with his teammates and coaches for a splashfest after the final scores were posted.
The 18-year-old diver looked every bit his age when he jumped up and down on the medals podium after being introduced to wild cheers.
"The crowd has been incredible," he said. "There are even people up there with Tom Daley masks on."
Daley came close to getting a medal in 10-meter synchro, but he and Peter Waterfield finished fourth. That result triggered malicious Twitter messages directed at Daley, including one that threatened him with drowning. A 17-year-old British man was arrested and issued a harassment warning.
Daley, one of the biggest faces of the London Games, badly wanted to win a medal in tribute to his father Robert, who died of brain cancer at 40 last year.
"I really wish my dad was here to see me do that performance because we had such a long, tough journey together," he said.
Daley's bronze was the first diving medal of any kind for Britain since 2004, when Waterfield and Leon Taylor won the 10-meter synchronized event, and it was the first individual medal since 1960, when the country won two bronzes.
It was quite a comeback for Boudia and Daley, who were inconsistent in the preliminaries on Friday night. Daley finished 15th, while Boudia grabbed the 18th and last spot for the semifinal. That left them with a lot of ground to make up to earn berths in the 12-man final.
But they returned to the pool Saturday morning looking like different divers. Boudia qualified third behind the two Chinese and Daley was fourth. Scores from the earlier rounds didn't carry over.
In the final, Daley got a do-over on his first dive after complaining that he was distracted by camera flashes in the stands.
The FINA judge reviewed the replay, which clearly showed several flashes going off, and allowed Daley to go back up the tower for another attempt.
He took advantage of his second chance, raising his score from 75.60 points to 91.80 on the back 2 1/2 somersault with 2 1/2 twists and into third.
Qiu, who was never lower than second after the second round, earned three 10s in the final.
Boudia earned one 10 on his fourth dive.
Victor Minibaev of Russia finished fourth. Jose Guerra of Cuba was just .10 points behind in fifth and earned one 10 in the competition. Lin Yue of China was sixth, falling from second after his third dive. He earned one 10 in the round.