The progress came after days of frustrating effort and, for the time being, removed a set of troubling options lying ahead for NASA and the Russian space agency if the computers continued to fail.
"They're up and operational and this is good news for all," said Lynette Madison, a NASA spokeswoman in Houston.
Cosmonauts Fyodor Yurchikhin and Oleg Kotov pulled off the feat by bypassing a power switch with a cable to get two out of three computer connections running. They planned to watch the computers for the next several hours to make sure they were functioning properly.
Had the machines continued to malfunction, the three-member space station crew could still have remained on board, but other steps would have been taken to maintain the power and oxygen supplies. Russia had already begun to move up plans for a cargo ship to deliver supplies, including new computers, next month.
And ominous questions were raised about the possibility of eventually needing to bail out of the space station — something a top NASA official rejected earlier in the say.
"It's more a question of the long-term health and survival of the space station itself. That's the critical issue here," reports CBS News space analyst Bill Harwood.
Maintaining the correct position in orbit is key for the space station. It must point its solar arrays at the sun for power and be able to shift orientation to avoid occasional large debris that comes flying through space.
The computer crash came as astronauts from space shuttle Atlantis were resuming work on the long-running construction of the station. Atlantis' seven astronauts arrived last weekend, NASA's first visit to the space station this year.
During the computer failure, the shuttles thrusters helped control the station's position. And some of Atlantis' lights, computers and cameras were turned off to save energy in case in case the shuttle had to spend an extra day docked to the station to allow more time to figure out the problem.
NASA officials said the crew was never in danger of running out of oxygen, power or essentials.
However, the failed computers were the latest technical glitch for the half-built, $100 billion outpost. In past years, a Russian oxygen machine and gyroscopes, which also control orientation, have failed.
Critics have called the space station a boondoggle, an ill-conceived, post-Cold War venture between the Super Powers which at the moment is producing little science as it undergoes construction.
The days-long computer problems fueled skepticism toward the Bush administration's "Vision for Space Exploration," which calls for finishing the space station in three years, grounding the space shuttles in 2010 and building next-generation vehicles to go to the moon and Mars.
"This growing chorus of opposition to the current vision ... is finding expression in the difficulties of the station," said Howard McCurdy, a space public policy expert at American University. "We're learning a great deal from the space station, and one of things we may be learning is we shouldn't have built this particular one."
Meanwhile, two Atlantis astronauts Friday had another mission to accomplish: repairing a torn thermal blanket that helps protect the shuttle from heat on its return flight to Earth.
Danny Olivas used a medical stapler to successfully secure in place the 4-by-6-inch corner, while James Reilly installed an external valve.
"Looking great!" Olivas said as he made rows of staples along the blanket's edge.
Plans for the 11-day mission were disrupted by discovery of the rip in the thermal material, a problem that extended the mission by two days so that Friday's repair spacewalk could be worked into the schedule.
For now, Atlantis is set to land at Cape Canaveral, Fla., on Thursday.