The drop occurred about an hour after the VMS Eve mothership took off from Mojave Air and Spaceport in Mojave, California.
The firm praised pilots Mike Masucci and Nicola Pecile for the "great milestone test flight". The mated vehicles climbed to a launch altitude of around 46,500ft over the Sierra Nevada Mountains before Eve executed a clean release of Unity.
The rocket went into a steep climb as the engine burned for 30 seconds and went supersonic, reaching Mach 1.87.
After the rocket motor shut down, the craft coasted to a maximum altitude of 84,271 feet (about 25,700 meters).
Aiming to be the world's first commercial spaceline, Richard Branson's Virgin Galactic launched a test flight of its SpaceShipTwo space plane, VSS Unity, on Thursday.
At around 50,000 feet, the pilots lowered the tail booms back into position. Both were employees of Scaled Composites, a Northrop Grumman subsidiary based in Mojave that built the vehicle.
Over 700 guests, including celebrities Katy Perry and Brad Pitt, have already reserved a seat on one of Virgin Galactic's first flights for a cost of $250,000 (£200,000) a seat.
The company noted that Unity has safety mechanisms that were developed after the accident.
While Unity has flown with the mother ship before, and has been released in glide tests, this is the first time it's fired up its rocket to fly on its own.
The tail booms are famous because "feathers" because their function has been likened to the feathers of the badminton shuttlecock.
"The flight has generated valuable data on flight, motor and vehicle performance which our engineers will be reviewing", Virgin Galactic said. The next phase of testing is also now ready to commence, which will expand the duration of the rocket burns to their full potential under the design. While the company celebrates that achievement, the team remains focused on the challenging tasks which still lie ahead.
A reusable space plane created to carry two pilots and up to six passengers (or research payloads) into suborbital space, the SS2 is Virgin Galactic's means for "transforming access to space", for paying customers and researchers, according to the company's vision statement.