"Time to wake up the patient and see how the big arm's doing after surgery," Mission Control said following the repairs by Franklin Chang-Diaz and Philippe Perrin.
About a half-hour later, after power coursed through the arm, Mission Control declared success.
"There have been surprises we encountered," Chang-Diaz radioed down. "But with everyone's help, we got the job done."
It was the first repair work done on the billion-dollar mechanical arm since its launch to the space station just over a year ago.
One of the three wrist joints in the Canadian-built high-tech construction crane seized up in March. NASA managed to work around the problem during a building project in April but wanted the joint replaced in case more trouble developed. Without a reliable robot arm, space station construction would come to a halt.
A replacement part arrived last week aboard space shuttle Endeavour.
Thursday's spacewalk, 240 miles above Earth, was the most challenging one yet for Endeavour astronauts Chang-Diaz and Perrin. They went out twice earlier in the week to install a movable platform for the robot arm and do other space station work.
To get to the wrist joint, Chang-Diaz and Perrin had to release six bolts and pull off the robot arm's bulky 4-foot-long hand. The wrist joint came off next with the loosening of six more bolts. Then the new wrist joint went on and the hand was reattached.
"Well, I got my workout today," Chang-Diaz said. "Miles to go before I sleep, they say is a poem. What is it? `The woods are dark and deep and I have promises to keep and miles to go before I sleep,"' he added, quoting from Robert Frost's "Stopping by Woods on a Snowy Evening."
At the end of the seven-hour spacewalk, Mission Control radioed up a recording of the Eagles' 1973 hit "Take it Easy." The song was played for the astronauts after each of their spacewalk-practice sessions on Earth.
Chang-Diaz thanked his trainers by name and told them: "This is the best time of my life."
Endeavour is scheduled to return to Earth on Monday after a 12-day mission during which it delivered a new three-member crew to the space.
CBS News Space Consultant William Harwood has covered America's space program full time for more than 15 years, focusing on space shuttle operations, planetary exploration and astronomy. Based at the Kennedy Space Center in Florida, Harwood provides up-to-the-minute space reports for CBS News and regularly contributes to Spaceflight Now and The Washington Post.