ROSWELL, N.M. — A man fell to Earth from more than 24 miles high Sunday, becoming the first human to break the sound barrier under his own power — with some help from gravity.

The man, Felix Baumgartner, an Austrian daredevil, made the highest and fastest jump in history after ascending by a helium balloon to an altitude of 128,100 feet. As millions around the world experienced the vertiginous view from his capsule’s camera, which showed a round blue world surrounded by the black of space, he stepped off into the void and plummeted for more than four minutes, reaching a maximum speed measured at 833.9 miles per hour, or Mach 1.24.

He broke altitude and speed records set half a century ago by Joe Kittinger, now 84, a retired Air Force colonel whose reassuring voice from mission control guided Mr. Baumgartner through tense moments. Engineers considered aborting the mission when Mr. Baumgartner’s faceplate began fogging during the ascent, but he insisted on proceeding and made plans for doing the jump blind.

That proved unnecessary, but a new crisis occurred early in the jump when he began spinning out of control in the thin air of the stratosphere — the same problem that had nearly killed Mr. Kittinger a half-century earlier. But as the atmosphere thickened, Mr. Baumgartner managed to stop the spin and fall smoothly until he opened his parachute about a mile above the ground and landed smoothly in the New Mexico desert.