Palin committed no major mistakes, but CBS News chief Washington correspondent Bob Schieffer gave the edge to Biden.
"I thought Sen. Biden had a very good night," Schieffer said. "Time and again, Gov. Palin would choose not to answer the question."
A CBS News instant poll of uncommitted voters who watched the debate also showed Biden to be the winner by a margin of 46-21 percent. About one-third thought the debate to be a draw.
But Palin's debate performance boosted her standing with these voters. Fifty-five percent said they now thought better of Palin. Fifty-three percent now think better of Biden.
Eighteen percent of the uncommitted voters say they now back Obama. Ten percent say they now support McCain. Seventy-one percent remain uncommitted.
As the much-anticipated debate unfolded, Palin accusedof voting against funding for U.S. troops in combat and chastised his Democratic running mate, Biden, for defending the move, "especially with your son in the National Guard" and headed for Iraq.
"voted against funding for the troops," as well, Biden countered, adding that the Republican presidential candidate had been "dead wrong on the fundamental issues relating to the conduct of the war."
Biden did not immediately reply to Palin's mention of his son, Beau, the Delaware attorney general, who is scheduled to fly to Iraq with his National Guard unit on Friday.
Palin also has a son who is serving in Iraq.
The exchange over Iraq was easily the most personal, and among the most pointed, as the two running mates debated for 90 minutes on a stage at Washington University in St. Louis.
They also clashed over energy, the economy, global warming and more in their only debate, with little more than one month remaining in the campaign and McCain struggling to regain his footing.
Biden was scathing in his criticism of McCain's position on the Iraq war, calling him the "odd man out" for his refusal to accept a timeline for the withdrawal of U.S. troops.
But Palin countered that a timetable was tantamount to "a white flag of surrender in Iraq," and at a moment when victory was "within sight."
She also said Biden had once supported McCain's view of the war, and noted that he once said Obama wasn't ready to be commander in chief ... "and I know again that you opposed the move that he made to try to cut off funding for the troops and I respect you for that."
"I don't know how you can defend that position now, but - I know that you know, especially with your son in the National Guard."
As for Obama, Palin said, "Another story there. Anyone I think who can cut off funding for the troops after promising not to - that's another story."
Biden's reply was in clipped tones. "John McCain voted to cut off funding for the troops. Let me say that again. John McCain voted against an amendment containing $1 billion, 600 million dollars" for protective equipment that is "protecting the governor's son and, pray God, my son and a lot of other sons and daughters. He voted against it."
CBSNews.com senior political editor Vaughn Ververs offered this analysis: "There may have been two candidate on stage tonight but all eyes were fixed firmly on the poltiical newcomer from Alaska, whose uneven performances in recent media interviews have raised questions about her qualifications for high office.
"While Palin stuck to her campaign talking points and, at times, veered away from the direct questions, she addressed a range of issues with the kind of specificity voters have not heard from her. It may not be enough to change opinions that have begun to turn against against her, but it could help soothe nervous Republicans who have taken to openly questioning her selection for the ticket."
"Biden proved that he's capable of getting past his penchent for committing gaffes and brought the full force of the three-plus decades in the U.S. Senate to bear in the debate," Ververs said. "He was effective in making his campaign's case against John McCain and avoided looking condescending towards Palin. Palin may have had the most to win or lose but Biden didn't do anything to hurt Barack Obama's cause."
Palin, who has been governor of her state for less than two years, was under intense pressure to demonstrate a strong grasp of the issues as she stepped onto the stage. Polls show the public has become increasingly skeptical of her readiness for high public office.
As is her custom on the campaign, she spoke in familiar terms, saying "betcha" rather than "bet you" and "gonna" rather than "going to."
She also spoke to the home folks. "Here's a shout-out" to third graders at Gladys Wood Elementary School in Alaska. She said they would all receive extra credit for watching the debate.
"Can I call you Joe?" she asked Biden as they shook hands before taking their places behind identical lecterns.
He readily agreed she could - and she used it to effect more than an hour later. "Say it ain't so, Joe," she said as she smilingly criticized him at one point for focusing his comments on the Bush administration rather than the future.
She made only one obvious stumble, when she twice referred to the top U.S. general in Afghanistan as "Gen. McClellan." In fact, his name is David McKiernan.
Biden's burden was not nearly as fundamental. Although he has long had a reputation for long-windedness, he is a veteran of more than 35 years in the Senate, with a strong knowledge of foreign policy as well as domestic issues.
For much of the evening, the debate unfolded in traditional vice presidential fashion - the running mates praising their own presidential candidate and denigrating the other.
Palin said Obama had voted to raise taxes 94 times - an allegation that Biden disputed and then countered. By the same reckoning, he said, McCain voted "477 times to raise taxes."
They clashed over energy policy, as well, when Palin said Obama's vote for a Bush administration-backed bill granted breaks to the oil industry. By contrast, she said that as governor, she had stood up to the same industry, and noted that McCain had voted against the bill Obama supported.
Biden said that in the past decade, McCain had voted "20 times against funding alternative energy sources and thinks, I guess, the only answer is drill, drill, drill."
"The chant is, 'drill, baby drill,'" Palin countered quickly, unwilling to yield to Biden on that issue - or any other.
On the environment, Palin declined to attribute the cause of climate change to man-made activities alone. "There is something to be said, also, for man's activities, but also for the cyclical temperature changes on our planet," she said, adding that she didn't want to argue about the causes.
Biden said the cause was clearly man-made, and added, "If you don't understand what the cause is, it's virtually impossible to come up with a solution."