The stubby rocket ship returned to Earth on Wednesday at 8.34am (1534 GMT), an hour-and-a-half after reaching the first stage of its bid to grab a $10 million prize aimed at kick-starting commercial space travel.
During its flight, SpaceShipOne reached an altitude of some 100km, jubilant organisers said, citing two unofficial radar readings.
At 14,100 metres, SpaceShipOne was released into a brief glide before pilot Michael Melvill fired its rocket motor and pointed the nose up towards space.
After a few minutes of weightlessness, it fell back into the atmosphere and glided back to the airport.
SpaceShipOne is trying for the $10 million Ansari X Prize, offered to whoever makes two flights 100km high, an altitude generally accepted as being in space, in two weeks or less.
A second flight is expected on Monday.
SpaceShipOne took off with a pilot and the equivalent weight of two passengers aboard, in accordance with rules requiring Ansari X Prize contenders to win.
Aerospace designer Burt Rutan, with more than $20 million from Microsoft billionaire Paul Allen behind him, secretly developed SpaceShipOne and is well ahead of two dozen teams building other Ansari X Prize contenders around the world.
The Ansari prize hopes to inspire
The prize is modelled after the $25,000 prize that Charles Lindbergh won in his Spirit of St Louis for the first solo New York-to-Paris flight across the Atlantic in 1927.
The St Louis-based Ansari X Prize Foundation hopes to inspire an era of space tourism in which spaceflight is not just the domain of government agencies such as Nasa.
Even before Wednesday's flight, airline mogul and adventurer Richard Branson announced in London on Monday that his Virgin Group plans to offer passenger flights into space aboard rockets based on SpaceShipOne by 2007.
Branson believes he will fly some 3000 people into space in the first five years that his "Virgin Galactic" space line is operating.