BEIJING — Seconds before the American men’s swimming team won gold by shattering the world record in the 4×100-meter freestyle relay at the Olympics yesterday, the man who swam the third leg, Bronx-born Cullen Jones, was fretting not about his time, or the competition, but simply hauling himself onto the deck.

“If you don’t get out of the pool by the next swimmer that comes in, you’re disqualified. My biggest goal was trying to make it to the ladder, because I was out of breath and I was afraid I was going to drown,” Jones told reporters yesterday.

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Jones made it out and turned around to see his teammate Jason Lezak, on his way to posting a lightning-fast 46.06-second time for the final leg, one that got him to the wall just eight-hundredths of a second before the final French swimmer, Alain Bernard.

“I saw Jason coming in, and it was the last 25 meters in and he was right there on the lane line, right next to Bernard, and I was just like, ‘Oh my God, please let him pull this off. Please let him pull this off. Come on. Come on. Come on.’ I was just screaming my head off,” Jones said.

The Americans took the gold with a time of 3:12.23, lopping almost four seconds off the world record, set by Jones and three other American swimmers just a day earlier. Still, the American performance was barely good enough yesterday in a stunning race in which all of the top-five teams bested the record.

“Swimming in general, especially in the sprints, we’ve just seen tremendous strides in times,” Jones said. The preternaturally good-natured swimmer bristled a bit when asked if the improvements were due to a new generation of swimsuits made with special materials that reduce drag.

“Is it the suit? The suit doesn’t get up at 5:30 in the morning, like I do. I’m not going to sit back and say, ‘Yes, the suit helped us.’ I refuse,” Jones said. “It doesn’t hurt, but it doesn’t make the swimmer come in first. We did that.”

It was the second gold of the Olympics for the leadoff swimmer, Michael Phelps, and kept alive the possibility of his winning eight golds, besting Mark Spitz’s record of seven in the 1972 games. Jones posted a split time of 47.65 seconds, which made him the least-fast of the Americans yesterday. Still, Jones gave Phelps a little ribbing for trailing the Australian team as the second American swimmer, Garrett Weber-Gale, hit the pool. “We had to, kind of, show up,” Jones joked.

Jones said he was still marveling at Lezak’s last-minute surge. “I guess a 46.0, the fastest split ever, definitely did help,” Jones said. “If I knew his secret, I would definitely do it myself. I have no idea. He just didn’t want to lose. He’s just that type of guy.”

Jones, 24, is the second swimmer of African-American descent to win Olympic gold, following Anthony Ervin, who took the gold in the same 4×100 event in the 2000 Olympics. Unlike Ervin, Jones, who lives in Irvington, N.J., talks openly about the lack of African-Americans in swimming. “The stigma of black people don’t swim, I think, is come to an end at this point,” Jones said yesterday.

However, when a reporter suggested a parallel to the presumptive Democratic presidential nominee, Senator Obama, Jones signaled that the talk of being a racial standard-bearer was going a bit too far. “Wow, you just made my shoes a little bit bigger. Thank you,” he said, rolling his eyes.

Jones credited his success to the devotion of his mother, Debra, and his father, Ronald, who died of cancer in 2000. “I had practice in New York and we lived in New Jersey. That’s an hour away. I had 5:30 in the morning practice, and we’d get up really, really early, and my parents would sit in the car and wait for me to finish practice. My friends always thought my parents were snipers,” Jones said. “I guess it paid off?” he said as he showed his medal to his mother at a center for athletes and their families set up by Bank of America.

Jones is planning a tour of America to encourage African-American and Hispanic youngsters to learn to swim, if only to be safe around water. “I can talk to kids all day. It’s more getting the parents to support it. The kids can’t get to practice on their own,” he said.

Last year was a tough one for Jones. He posted strong times, but had trouble beating out his teammates. Then, in November, at a key 50-meter race in Georgia, he came in eighth after his goggles flipped up when he hit the water.

“In the past year, I did have quite a few downs affecting my career. I wouldn’t say that I wasn’t swimming well. I just wasn’t swimming to the expectations of other people and also to myself,” Jones said in response to a question from The New York Sun. Within a few months, he decided to leave his alma mater and train with a new coach at Charlotte, N.C. “It was definitely a great change for me, and that’s when I started to see a little bit more positive,” he said.