People living along the central Atlantic coast of Florida have for decades enjoyed the spectacle of rockets headed for space. On Monday night, they were treated to a new sight that may become common: a rocket coming back down to a gentle landing.

“It really felt like it was right on top of us,” Elon Musk, the chief executive of Space Exploration Technologies Corporation of Hawthorne, Calif., or SpaceX for short, said during a telephone news conference afterward.

With the rush of sound from the rocket engines, Mr. Musk, who was at the launch site in Florida, said he initially thought the landing was a failure, ending with an explosion. But then he heard from mission control that the booster was standing, in one piece.

For SpaceX, the 8:29 p.m. liftoff of the Falcon 9 rocket from Cape Canaveral Air Force Station was a threefold success.