The Dragon will remain at the space station for most of March before returning to Earth with science samples, empty food containers and old equipment.
The California-based SpaceX run by billionaire Elon Musk has a $1.6 billion contract with NASA to keep the station well stocked. The contract calls for 12 supply runs; this was the second in that series.
This is the third time, however, that a Dragon has visited the space station. The previous capsules had no trouble reaching their destination. Company officials promise a thorough investigation into what went wrong this time; if the maneuvering thrusters had not been activated, the capsule would have been lost.
Ford said everything about Sunday's rendezvous ended up being "fantastic."
"There sure were some big smiles all around here," NASA's Mission Control replied from Houston.
Proclaimed SpaceX on its web site: "Happy Berth Day."
In a tweet following Friday's nerve-racking drama, Musk said, "Just want to say thanks to (at)NASA for being the world's coolest customer. Looking forward to delivering the goods!"
Musk, who helped create PayPal, acknowledged Friday that the problem -- the first ever for an orbiting Dragon -- was "frightening." But he believed it was a one-time glitch and nothing so serious as to imperil future missions. The 41-year-old entrepreneur, who also runs the electric car maker Tesla, oversaw the entire operation from Hawthorne, Calif., home to SpaceX and the company's Mission Control.
The Dragon's splashdown in the Pacific, off the Southern California coast, remains on schedule for March 25.
NASA is counting on the commercial sector to supply the space station for the rest of this decade; it's supposed to keep running until at least 2020. Russia, Europe and Japan are doing their part, periodically launching their own cargo ships. But none of those craft can return items like the Dragon can; they burn up on re-entry.
Russia also is providing rides for astronauts -- the only game in town since the retirement of NASA's space shuttles in 2011.
SpaceX, or more formally Space Exploration Technologies Corp., leads the commercial pack that is working toward launching astronauts in another few years. Musk said he can have people flying on a modified Dragon by 2015.
NASA's shuttles used to be the main haulers for the space station. At the White House direction, the space agency opted out of the Earth-to-orbit transportation business in order to focus on deep space exploration. Mars is the ultimate destination.