With a near-flawless docking on Friday, start-up rocket company SpaceX achieved what only big governments have to date: It launched a mission to the international space station.

The moment marked a pivot point in U.S. space ambitions, away from total NASA control and toward creative private enterprise. While NASA furnished seed money and technical advice, SpaceX engineers designed, built, launched and drove the white gumdrop-shaped Dragon capsule until the final moments.

While the docking marked a milestone, it was more a policy win than a technical achievement: Shooting stuff into space has been routine for 50 years, and the Dragon carried no astronauts. That is a bigger mission that SpaceX and other U.S. companies are now racing toward.

“Launching cargo, difficult as it is, is much less difficult than launching humans,” said NASA astronaut Clayton Anderson, who spent five months on the space station in 2007. “SpaceX still has some challenges to get through.”

But the docking did help validate a space policy that’s drawn scorn and hope. Former and current astronauts, legislators and policymakers have questioned whether the private sector can launch a vehicle with brute force and then delicately pirouette it around a football-field-size orbiting outpost.

SpaceX controllers did both this week and made it look easy.

“It’s been a remarkable ride,” Michael Suffredini, NASA’s space station manager, said shortly after Dragon’s docking.

After a two-hour delay to fix a balky laser range finder on Dragon, two station astronauts — American Don Pettit and Dutchman Andre Kuipers — lassoed the capsule with a giant robotic arm at 9:56 a.m.

“Looks like we’ve got us a dragon by the tail,” Pettit quipped from 250 miles above Australia.

Cheers erupted in two mission control rooms — at NASA in Houston and SpaceX headquarters near Los Angeles.

Video feeds showed the casually dressed SpaceX team high-fiving and hugging. Elon Musk, the company’s usually voluble founder, later said he had no words for the “moment of elation.”

Two hours later, the station astronauts snuggled Dragon into a docking port.

Mission nearly complete.

“In my 20 years with NASA, rarely did things go that smoothly,” said Michael Lopez-Alegria, a former space station commander and president of the Commercial Spaceflight Federation, an industry group. “And they never go that smoothly the very first time.”

He added, “I’m not sure I would’ve put money on it two weeks ago.”

He had reason to worry. Conceived in 2006 as a space shuttle replacement, NASA’s commercial spaceflight program is three years behind schedule. The SpaceX mission was repeatedly delayed since last year, most recently Saturday, when the Falcon 9 rocket’s engines fired and then squelched on the launchpad because of a bad valve.

But on Tuesday, the rocket finally soared atop an arc of orange. It was the second SpaceX mission for the Dragon capsule. In December 2010, a Dragon orbited the Earth and splashed down off the California coast.

On Friday, Musk sat in front of that first, scorched Dragon as SpaceX workers chanted his name, shouting, “We love Elon!”

For weeks, the Internet millionaire had been scaling back expectations, saying this was a test flight, a shake-down mission.

But at a post-docking news briefing, Musk beamed and repeated his ambition to fly people to Mars and beyond. “This was a crucial step,” he said, toward spreading humanity to other planets. “The chance of that just went up dramatically.”

While more circumspect, NASA and White House officials also heralded the day.

Presidential science adviser John P. Holdren, in a statement, called the moment “an achievement of historic scientific and technological significance” and “a key milepost in President Obama’s vision for America’s continued leadership in space.”

NASA administrator Charles F. Bolden Jr., attending the International Space Development Conference in Washington, watched on a video screen and exclaimed, “We have berthed!”

Friday’s success edges SpaceX closer to sending astronauts back into orbit from American soil. After retiring its space shuttles last year, NASA now relies on Russia to ferry astronauts to and from the station — at $63 million a seat. Last year, the agency funded four U.S. companies, including SpaceX, to build a space vehicle safe enough for humans.

But NASA and the Obama administration are battling Congress over funding. The administration wants $800 million for the commercial crew program next year, but the House of Representatives wants to cut that nearly in half. NASA’s Bolden has vehemently pushed back.

On Friday, Musk said that SpaceX could be ready to fly people into space by 2015.

But Scott Pace, a space policy expert at George Washington University and an adviser to Republican presidential candidate Mitt Romney, said the company first needs a track record. “They need to fly [cargo] six or seven times consecutively,” he said.

With nearly 2,000 employees, SpaceX is ramping up production to fulfill $4 billion in contracts, with NASA just one of their customers. The company is young — the average employee age is 30 — and Musk said he’s picked a team that balances “the wisdom of age with the vibrancy of youth.”

Their next mission — the first of 12 deliveries to the station — is slated for September.

Meanwhile, a local company, Orbital Sciences of Dulles, is preparing a new launchpad on Wallops Island, Va., to send its new cargo carrier to the space station late this year.

The two companies are slated to make the bulk of cargo runs in the future to the station, which is now supplied by Russia, Japan and the European Union.

Along with food, water and computers, the Dragon carried a tiny cargo that began its journey in the District: two vials with a waste-purifying experiment designed by eighth-graders at ­Stuart-Hobson Middle School. Station astronauts will snap the vials like glow sticks, mingling bacillus bacteria with egg white.

Kyra Smith, the 14-year-old D.C. Public Schools student who conceived the experiment, said, “I’m interested in environmental conservation, so I thought astronauts that go up into the space station could reuse water and save space on their rockets.” If her experiment works, the bacteria will clear out the egg white — which is standing in for human waste. The experiment is one of 15 on the Dragon chosen from among 800 schools.

The program was started by the nonprofit National Center for Earth and Space Science Education in Capitol Heights to give students experience running experiments.

On Thursday, Dragon is scheduled to depart the station, carrying Smith’s vials along with frozen blood and urine from astronaut biology experiments and old spacesuit parts. If all goes well, it will splash down in the Pacific later that day.