Virgin Galactic founder Richard Branson made the voyage on July 11, narrowly beating the Amazon magnate in their battle of the billionaires.
But Blue Origin's sights were set higher: both in the altitude to which its reusable New Shepard craft would ascend compared to Virgin's spaceplane, and in its ambitions.
Bezos, 57, founded Blue Origin in 2000 with the goal of one day building floating space colonies with artificial gravity where millions of people will work and live.
Today, the company is developing a heavy-lift orbital rocket called New Glenn and also a Moon lander it is hoping to contract to NASA.
Named after Alan Shepard, the first American in space, the New Shepard suborbital rocket had flown 15 uncrewed flights to put it through its paces and test safety mechanisms.
Lift-off was slightly delayed and came at 1312 GMT from a remote facility in the west Texas desert called Launch Site One, some 25 miles (40 kilometers) north of the nearest town, Van Horn.
"This might have looked easy today, it was anything but easy," said Gary Lai, lead designer of New Shepard.
Richest, oldest, youngest
Notably absent was the still anonymous winner of a $28 million auction for a seat, who had "scheduling conflicts" and will take part in a future flight.
Daemen's father, the CEO of a private equity firm, was a runner-up in the bidding, allowing his teenage son to become the company's first paying customer.
After lift-off, New Shepard careened towards space at speeds exceeding 2,300 mph (3700 kph) using a liquid hydrogen-liquid oxygen engine whose only byproduct is water vapor.
The capsule separated from its booster, and when it got high enough, the astronauts unbuckled and experienced space for three to four minutes.
The booster returned autonomously to a landing pad just north of its launch site, while the capsule fell back to Earth with three giant parachutes, and finally a thruster, for a gentle landing.
'Read the room'
Blue Origin has remained relatively coy about what comes next.
The company says it plans two more flights this year, then "many more" next year.
Analysts say much will hinge on early successes and building a solid safety record.
CEO Bob Smith revealed Sunday that the next launch could take place in September or October, adding "willingness to pay continues to be quite high."
At the same time, the sector is beginning to face criticism over the optics of super wealthy individuals blasting off to space while Earth faces climate-driven disasters and a coronavirus pandemic.
"Could there be a worse time for two uber-rich rocket owners to take a quick jaunt toward the dark?" wrote Shannon Stirone in an Atlantic piece titled "Space Billionaires, Please Read the Room."
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© 2021 AFP