Endeavour and its crew of seven rose from the seaside pad at 6:36 p.m. (2236 GMT), right on time, and pierced a solidly blue sky. They were expected to reach the international space station on Friday.
Once Endeavour was safely past the 73-second mark of the flight, the moment when Challenger exploded shortly after the call "Go at throttle up," Mission Control exclaimed, "Morgan racing toward space on the wings of a legacy."
Immediately after the shuttle reached orbit, Mission Control announced, "For Barbara Morgan and her crewmates, class is in session."
Morgan was McAuliffe's backup for Challenger's doomed launch in 1986 and, even after two space shuttle disasters, never swayed in her dedication to NASA and the agency's on-and-off quest to send a schoolteacher into space. She rocketed away in the center seat of the cabin's lower compartment, the same seat that had been occupied by McAuliffe.
McAuliffe's mother, Grace Corrigan, watched the launch on TV from her home in Massachusetts. "I'm very happy that it went up safely," she said. "We all send her our love," she added, her voice breaking.
• Click here to visit FOXNews.com's Space Center.
More than half of NASA's 114 Teacher-in-Space nominees in 1985 gathered at the launch site, along with hundreds of other educators, all of them thrilled to see Morgan continue what McAuliffe began.
Also on hand was the widow of Challenger's commander, who said earlier in the day that she would be praying and pacing at liftoff and would not relax until Morgan was safely back on Earth in two weeks.
"The Challenger crew — my husband, Dick Scobee, the teacher Christa McAuliffe — they would be so happy with Barbara Morgan," said June Scobee Rodgers. "It's important that the lessons will be taught because there's a nation of people waiting, still, who remember where they were when we lost the Challenger and they remember a teacher was aboard."
NASA Administrator Michael Griffin met Tuesday night with several members of the Challenger astronaut families in town for the launch — although not the McAuliffe family — and said they did not seem worried.
"They didn't act like they came to see another tragedy," he said. "They're here to celebrate her having a chance to fly."
Griffin knows better than most that NASA could lose another teacher in flight.
"Every time we fly I know that we can lose a crew," he told The Associated Press early Wednesday afternoon. "That occupies a large portion of my thoughts. Unless we're going to get out of the manned space flight business, that thought is going to be with me every time we fly."
Midway through the flight, Morgan, 55, will speak with students in the northern state of Idaho, where she taught elementary classes before moving to Houston in 1998 to train as a full-fledged astronaut, the first teacher to do so. If the mission is extended from 11 days to 14 days as planned, thanks to a new station-to-shuttle power converter, she'll have a chance to answer questions from students in two other states.
But Morgan's main responsibility in orbit will be to her commander, Navy Cmdr. Scott Kelly. She will help operate Endeavour's robot arm and oversee the transfer of cargo from the shuttle to the station. The rest of the crew will be busy installing a huge square-shaped beam to the exterior of the station and replacing a broken gyroscope. Three and possibly four spacewalks are planned.
Endeavour's astronauts also will use a 50-foot (15-meter) laser boom on the end of the robot arm to inspect the shuttle's wings, nose and belly. The scan for damage from fuel-tank insulating foam and other debris from launch, or micrometeorites in space, has been standard procedure ever since Columbia's catastrophic re-entry in 2003.
The space station is currently almost 250 tons and 57 percent complete. By the time Endeavour leaves, the station will have several more tons permanently attached to its frame. NASA plans to wrap up construction in 2010 when the shuttle program ends.
NASA is hoping a successful flight will draw some attention away from the rash of embarrassments it has faced this year, most recently a NASA-commissioned medical panel's report suggesting astronauts were intoxicated on launch day on at least two occasions.
Griffin said Wednesday that NASA is investigating the anonymous allegations. The space agency's top safety official has gone back 10 years through every shuttle flight and can find no flight surgeon, astronaut or document hinting at launch day drinking by a crew member, he said.
"This is not a credible scenario. They're on TV. We just watched them having breakfast," Griffin said, referring to the Endeavour astronauts.
"The charges seem uncredible, and it also seems uncredible that somebody would just make it up. That's why it's so puzzling and that's why it's serious and that's why we will investigate."
Endeavour's liftoff had been scheduled for Tuesday, but last week NASA delayed the flight by a day because of a leaky valve in the crew cabin that needed to be replaced.
This is Endeavour's first flight since 2002. The shuttle underwent a massive overhaul and was outfitted with complete satellite navigation, improved main engine monitoring equipment, and a new system for transferring power from the station to the shuttle. The extra power will allow the shuttle to remain docked at the space station longer than ever before.
Besides Morgan and Kelly, the commander, the crew includes Marine Lt. Col. Charles Hobaugh, the copilot; Rick Mastracchio, Tracy Caldwell, Air Force Col. Alvin Drew and Canadian physician Dave Williams.