During the test flight, it carried four NASA research payloads and a mannequin name Annie as a stand-in passenger.
Numerous crowd embraced and cried as the rocket plane made its landing.
A successful flight will be significant progress toward the start of commercial flights that Virgin Galactic promised more than a decade ago.
One pilot lost his life and another was seriously injured in 2014 after the SpaceShipTwo crashed during a test flight.
Virgin Galactic wound up surpassing its previous record of 32.3 miles from July's test flight and reached just below the Kármán line at 62 miles above Earth, which marks the boundary between the upper atmosphere and outer space.
And, the firm said the "results are good".
Virgin's Thursday launch likely will not go as high as the Karman line. In the same Mojave hangar where VSS Unity and WhiteKnightTwo were being prepared for flight, other employees were working on two new SpaceShipTwo vehicles.
"During this phase of the flight program we will be expanding the envelope for altitude, air speed, loads, and thermal heating".
The flight - with two pilots on board - was a major victory for the company headed by British tycoon Richard Branson, who is striving to send tourists to space at a cost of $250,000 per seat.
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Engineers did not plan for a full duration burn, leaving the eventual altitude up to sweaty-palmed boffins on the ground and the pilots at the pointy end of things as the craft's handling characteristics and thermal dynamics were carefully monitored.
Sir Richard is battling other billionaire-backed ventures to offer space flights to tourists, including one from Amazon founder Jeff Bezos' Blue Origin.
The multi-millionaire admitted earlier this year that the number of spurious claims he has made about Virgin Galactic flight dates was "embarrassing".
The company is hoping to launch its fourth powered test flight with more ambitious conditions when its window opens on December 13th.
"There is no guarantee that everything will work perfectly first time and, like all programs seeking to take bold steps, we will inevitably have times when things don't go as planned". After a 60-second engine burn speeds the craft to almost three times the speed of sound, it continues its ascent, coasting until it reaches maximum altitude.
"It was a great flight and I can't wait to do it again", said Sturckow, who flew on the space shuttle four times. The space agency has lacked that capability for more than seven years. The company aims to take paying customers on the six-passenger rocket, which is about the size of an executive jet. The rocket is shut down and the craft coasts to the top of its climb - and then begins a descent slowed and stabilized by unique "feathering" technology.
The carrier airplane hauled the SpaceShipTwo passenger rocket plane to an altitude of about 45,000 feet (13.7 kms) and released it. Seconds later, SpaceShipTwo fired, catapulting it to more than 51 miles (82 km) above Earth, high enough for the pilots, Mark Stucky and Frederick Sturckow, to experience weightlessness and see the curvature of the planet.
The total trip time would last between 90 minutes and two hours.