The company founded and led by Mr Musk normally recovers its boosters, landing them upright on a floating platform or back at the launch site.
"This critical flight test puts us on the cusp of returning the capability to launch astronauts in American spacecraft on American rockets from American soil", said NASA Administrator Jim Bridenstine.
SpaceX has blown up a missile in Florida on Sunday in a final test launch of its Crew Dragon space capsule, showing that it can bring astronauts to safety in an emergency launch.
After about 87 seconds, the Crew Dragon, who did not carry astronauts for this test, set up his eight SuperDraco engines to fire him at a safe distance from the rocket - exactly as he was created to do if there was a serious deviation during the take-off of the rocket on a future manned mission. It's expected to be the last major milestone in Crew Dragon's development program before the spacecraft is deemed ready to begin sending astronauts to space.
Shifting back to Demo-2, along with heading to the ISS, NASA says the mission could run longer than expected depending on what both firms plans are.
A successful emergency abandonment test will mark an important victory for SpaceX.
Rough seas and high winds forced SpaceX to stand down from a planned test flight of the abort system on its Crew Dragon spacecraft.
Boeing suffered a setback when its Starliner spacecraft malfunctioned during an orbital test flight in December, and it's not clear when the vehicle will be ready for crewed missions.
The rocket that was mostly destroyed Sunday included the first booster ever flown of SpaceX's latest rocket type, the Falcon 9 Block 5, which had its maiden launch in May 2018.
Musk said he was "super fired up" by the successful test.
"It is a picture flawless mission". Air Force and SpaceX teams were stationed to fix it while they were rehearsing to remove a crew from the capsule. Lueders said SpaceX would conduct at least two additional tests of the Crew Dragon parachute system in the coming days.
Preferring to focus on the moon and Mars, NASA hired SpaceX and Boeing for billions of dollars to transport astronauts to and from the space station.
The capsule has already demonstrated it can fly into orbit and autonomously dock with the International Space Station: It completed an uncrewed demonstration mission in March 2019. The parachutes on this Crew Dragon were SpaceX's newest version, the Mark 3 parachute design.
Boeing will not perform a test similar to the SpaceX abandonment flight test. Lueders said Friday that each company is allowed to design its own test programs and "everyone has their benefits". At a post-test press conference, SpaceX Chief Executive Elon Musk announced that it was feasible that the flight will take place in the second quarter of this year.