Sir Richard Branson was watching as SpaceShipTwo – known as VSS Unity – landed about 10 minutes after detaching from its carrier aircraft.
The carrier – WhiteKnightTwo – also made it safely back to the ground.
It comes more than two years after a man was killed when the first craft crashed during a powered test flight.
An investigation last year by the National Transportation Safety Body found the October 2014 accident was caused by a catastrophic structural failure.
It was triggered when co-pilot Michael Alsbury unlocked the craft’s braking system early.
Mr Alsbury was killed and pilot Peter Siebold seriously injured when the spaceship broke apart – again over the Mojave Desert.
As this weekend’s test got underway, British astronaut Tim Peake tweeted: “Good luck with this new phase of the test programme @virgingalactic – safe flight #pushingboundaries.”
Sir Richard, the Virgin Group founder, was with Virgin Galactic chief executive George Whitesides as the test was carried out.
The two men were later pictured congratulating Chief Pilot Dave Mackay and Test Pilot Mark Stucky.
There will be further glide flights, after which the team will check the Unity’s hybrid motor during rocket-powered tests.
Virgin Galactic has said it will begin a commercial operation from Spaceport America in New Mexico “once it believes it is safe to do so”.
It will also need regulatory approval.