LONDON — Eyeing the trackside clock as she approached the finish line, Carmelita Jeter pointed the black baton in her left hand at those bright orange numbers.

She wanted to make sure everyone saw what she saw: The United States was breaking the world record in the women’s 4x100-meter relay — and it wasn’t even close.

Allyson Felix, Tianna Madison and Bianca Knight built a big lead, and Jeter brought it home Friday night, anchoring the U.S. to its first Olympic gold medal in the sprint relay since 1996 with a time of 40.82, more than a half-second better than a record that had stood for 27 years.

“As I’m running, I’m looking at the clock and seeing this time that’s like 37, 38, 39. In my heart, I said, ‘We just did it!’ I definitely knew we ran well,” Jeter said. “When I crossed the finish line, I had so many emotions because we haven’t been able to get the gold medal back to the U.S.”

Felix collected her second gold of the London Games, along with the one she won in the 200 meters, while Jeter completed a set, adding to her silver in the 100 and bronze in the 200.

“I just knew if we had clean baton passes that we would definitely challenge the world record. Smash it like we did? We had no idea,” Madison said, “but I knew it was in us.”

The American quartet erased the old mark of 41.37 run by East Germany in October 1985. Here’s how long ago that was: Jeter was 5, Madison was a month old, and Felix and Knight weren’t even born.

“It’s an absolutely unreal feeling. It just feels like for so long, we looked at women’s sprints and the records were so out of reach. To look up and see we had a world record, it was just crazy,” said Felix, who gets a shot at a third gold in the 4x400 final today. “I didn’t think that was going to happen.”

Jamaica won the silver medal in a national record of 41.41 seconds, with a team of 100 champion Shelly-Ann Fraser-Pryce, 100 bronze medalist Veronica Campbell-Brown, Sherone Simpson and Kerron Stewart.

“All their girls are in top shape this year. You can’t say they didn’t deserve it. They prepared for it and they came out here and they delivered,” Fraser-Pryce said. “For us, it’s back to the drawing board.”

The bronze went to the Ukraine in 42.04.

Madison ran the opening leg, and Felix the second. Then, with Knight approaching for the final handoff, Jeter took nine strides, reached her hand back and took a perfect exchange. Jeter was staring at the clock as she covered the final 10 meters — and she jutted the stick in that direction.

“I saw the huge lead that we have, and I looked up on the board and saw the time flash, and I was so confused,” Felix said. “I was like, ‘That is not a 4x100 time.’ I was waiting, and then I saw the world record, and I was like, ‘This is insane.’ It was just a beautiful thing to see. As soon as Bianca passed to ‘Jet,’ it was done.”

Afterward, the quartet of champions paused to watch a replay of their record performance on the scoreboard at 80,000-seat Olympic Stadium. When Jeter was shown crossing the finish line, Knight punched the air.

The perfect trip around the track ended a string of disappointments for the U.S. in the event.

In Athens eight years ago, Lauryn Williams was involved in a bad exchange in the final, leaving her team without a medal. In Beijing four years ago, the Americans didn’t even reach the final because Torri Edwards and Williams bobbled the last exchange in the semifinals. That marked the first time since 1948 that the U.S. wasn’t involved in the women’s 4x100 medal race at the Summer Games.

This time they were back in the final — and now they’re champions again, too.

“It’s a relief. It’s a joy. It’s everything,” Felix said. “We went into this race and it was the most comfortable I’ve seen this team. We were laughing and smiling. We’ve never been like that. We were confident. We felt good. We were confident in the passes, and it showed.”

And Williams even gets a gold medal this time, because she ran a leg in Thursday’s semifinal.

“Talking about the ‘botched handoff’ is history now,” Madison said. “She has completely obliterated that from her record.”

The U.S. performance was part of a speedy night on the track, even if Usain Bolt wasn’t around: The U.S. and Jamaica turned in two of the five fastest men’s 4x100 relays in history to set up a showdown in today’s final.

And in the 4x400, Ramon Miller of the Bahamas overtook Angelo Taylor of the United States to give his country its first men’s Olympic gold medal in any sport.

Miller powered Bahamas to a time of 2:56.72, 0.33 seconds better than the U.S., which had won that event at every Olympics since 1984. Trinidad and Tobago took third.

The United States was missing three injured runners, including Manteo Mitchell, who finished out his preliminary lap Thursday on a broken leg and was there to watch Friday, leaning on crutches.

“Without him, this wouldn’t be possible,” said Tony McQuay, Mitchell’s roommate in the athletes village. “He held it down for the USA. Sorry we couldn’t give him the gold.”

The South African team finished last, falling way behind before double-amputee Oscar Pistorius even got his hands on the baton for the anchor leg.

In the 4x100 semifinals, dash bronze medalist Justin Gatlin ran the anchor leg as the Americans broke a 20-year-old national record by finishing in 37.38 seconds. The old mark of 37.40 was initially established in 1992 with Carl Lewis on the last leg, and later equaled.

Jamaica ran 37.39 in the other semifinal — and that was without Bolt, who got a chance to rest a day after adding gold in the 200 to his gold in the 100 but is expected to run the anchor in today’s final.

“We’re going to figure out a way to go out there and compete with them,” Gatlin vowed. “We’re not scared of them.”

The current world record of 37.04 was set by Jamaica at last year’s world championships.