While no people were on board, the flight represents a significant step for NASA.
The mission, called Demonstration-1 or DM-1, is meant to show NASA that Crew Dragon is safe for future human crew members. And if all goes well, a flight with humans could happen as soon as this year.
After the Space Shuttle program retired in 2011, NASA turned for the first time to the private sector to build the next generation of human spaceflight hardware. It follows an eight-year lapse from the last flight of the Space Shuttle during which America has bought seats on Russian Soyuz rockets for crew trips to the station.
In a risky experiment, NASA years ago made a decision to outsource transportation to what's known as low Earth orbit to the private sector.
If successful, the mission launched on Saturday and the upcoming manned launch will allow NASA to certify the new spacecraft for regular flights to the space station.
The capsule successfully separated from the rocket about 11 minutes later, sparking cheers in the control room, and began its journey to the space station. "But it worked - so far".
The excitement was palpable Friday at Cape Canaveral, where a day earlier the rocket was wheeled out of its hangar and staged in a vertical position on the legendary launch pad where the Apollo Moon missions took off.
It's been a momentous Saturday for SpaceX, and for the future of crewed voyages into space. But despite all its successes, the company has yet to fly astronauts.
Although the Dragon capsule itself is created to carry a crew of up to seven astronauts skyward, the one that launched on Saturday - Demo-1 is its designation - is more of a test run: it's carrying a few hundred pounds of cargo, plus a sensor-filled dummy named "Ripley".
In 2014, the United States space agency awarded contracts to SpaceX and Boeing for them to take over this task.
Bridenstine said he's confident that astronauts will soar on a Dragon or Starliner - or both - by year's end.
The video is titled Crew Demo-1 Mission. Boeing's first flight with people is scheduled for August. Many officials have warned that since the program is still in the test phase the schedules are likely to slip, perhaps even significantly.
At Saturday's post-launch news conference, Musk said he'd be happy to fly on the revamped Dragon. SpaceX has been developing Crew Dragon under a $2.6 billion commercial-crew contract with NASA, after all.
Though Demo-1 is astronaut-free, Crew Dragon is carrying one lifeless - but lifelike - passenger, a dummy outfitted with a variety of sensors so scientists can measure the forces exerted on the body during the mission. "I went over and asked what they thought, and how they felt about flying on it", Musk said.
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May has repeatedly ruled this out, saying it would undermine faith in democracy among the 17.4 million who voted in 2016 to leave. The EU law says that batch testing of products sold in the EU needs to be carried out in one of the member states.
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But the SNP's Westminster leader Ian Blackford said: "Another day, another resignation from the United Kingdom government". May says United Kingdom lawmakers will get to vote again on her deal - including any amendments she secures - by March 12.