After about 14 orbits of the Earth, the craft, more than 50 meters tall, re-enters the atmosphere at high speed.
Elon Musk's company fails, however, to recover as planned the lower stage, the booster named Super Heavy.
This maneuver marks a milestone for the project of a fully reusable rocket intended for journeys to the Moon and to Mars.
It returns to the Texas base from which it took off, before an enthusiastic crowd.
The operation is far more complex and risky than the recovery already practiced by SpaceX on a lower stage: the upper stage falls back from much higher and much faster.
Although it has already succeeded in this recovery three times in the past, it abandons the attempt shortly after launch because of a technical problem.
SpaceX must still make sure that the spacecraft was not too badly damaged by its return into the atmosphere.
It also remains to be verified that it can be reused without major work, as was the case with NASA's former space shuttles.
Starship, the largest and most powerful rocket ever built, is also designed to send data centers into space.