The move marks the California firm's entry into the commercial satellite market which is globally worth nearly $190bn (£116bn) a year.
The $100m (£61m) telecommunications satellite, owned by Luxembourg-based SES, was launched on top of SpaceX's upgraded Falcon 9 rocket from Cape Canaveral in Florida.
Until now, SES satellites have primarily been taken up on Russian Proton and European Ariane rockets.
They cost far more than the $55m (£33m) the company paid for its ride on SpaceX's Falcon booster, SES spokesman Martin Halliwell said.
"The entry of SpaceX into the commercial market is a game-changer. It's going to really shake the industry to its roots", he added.
More than 20,000 miles above Earth, the three-ton SES-8 satellite will provide TV, broadband and other communications services to customers in India, China, Vietnam and elsewhere in Asia.
Two previous launch attempts last week were scuttled by technical glitches, including a last-second abort on Thursday.
Engineers later discovered oxygen inside the unmanned rocket's ground-based engine igniter system.
"I'd like to thank SES for taking a chance on SpaceX," company founder and chief executive Elon Musk posted on Twitter an hour before the launch.
"We've given it our all."
Afterwards, he said the delivery of the satellite "confirms the upgraded Falcon 9 launch vehicle delivers to the industry's highest performance standards".
He added: "We appreciate SES' early confidence in SpaceX and look forward to launching additional SES satellites in the years to come."
SES operates the world's second biggest satellite fleet - 54 in all.
SpaceX has launched six Falcon 9 rocket missions since the booster's debut in 2010.
But most of those were either test flights or missions for Nasa to deliver cargo to the International Space Station using the company's unmanned Dragon spacecraft.
SpaceX has a $1.6bn (£733m) contract to fly 12 cargo missions to the space station for Nasa. Two of those delivery flights have already been launched.
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