Engineers played down the incident, but it renewed recent questions about Russia's otherwise famously reliable spacecraft.
Vladimir Solovyov, flight director for the Federal Space Agency, said that just a few minutes before the docking time an autopilot signal went off showing that one of Soyuz engines might have failed.
Cosmonaut Gennady Padalka reported that the engines were operating normally, and he took manual control of the capsule to keep an emergency computer program from thrusting the engines and sending the craft backing away from the station.
"We took the decision not to allow that," Solovyov told a news conference at mission control in Korolyov, on Moscow's outskirts.
"We have to figure out what happened," he said.
The docking by Padalka appeared otherwise smooth and was slightly ahead of schedule, roughly two days after the capsule blasted off from the Baikonur Cosmodrome in Kazakhstan's barren steppe. Applause broke out among space officials and crew relatives gathered at mission control after the hookup was announced.
Cosmonauts typically receive extensive training in the event that Soyuz's autopilot fails or some other problem pops up.
"Everyone worked wonderfully, on the ground and on the spacecraft. There were no uncontrolled situations," said Vitaly Lopota, chief engineer with Soyuz manufacturer RKK Energia.
Padalka and U.S. astronaut Michael Barratt are joining the station's current crew, while Simonyi, who is making his second trip as a paying customer to the space station, returns to Earth on April 7 along with cosmonaut Yury Lonchakov and NASA astronaut Michael Fincke.
Some three hours after docking, the crews opened the hatches and Padalka, Barratt and Simonyi floated in to greet the station's occupants -- Japanese astronaut Koichi Wakata, NASA astronaut Michael Fincke and cosmonaut Yury Lonchakov -- with hugs, smiles and handshakes.
"We had a great ride up here, and the docking was a little bit of excitement, but we're very glad to be here and the station looks great," Barratt said later in a video hookup with mission control.
"It was an awfully fun ride," he said after wishing his wife Michelle a happy anniversary.
Simonyi, a Hungarian-born software designer, exchanged greetings with his brother in Hungarian. Padalka's daughter sang a small song while Padalka played with a small stuffed animal that floated about the station's compartment.
Saturday's incident was the latest of several mishaps in recent years to hit Russia's spacecraft, which otherwise have a reputation for reliability and safety.
Last year, a Soyuz capsule returning from the station landed hundreds of kilometers off target in Kazakhstan after hurtling through Earth's atmosphere in a steeper-than-normal descent that subjected the crew to severe G-forces.
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