CONCORD, N.H. -- New York Sen. Hillary Rodham Clinton proved Tuesday that more than one Clinton can be "the Comeback Kid," clearly basking in a decisive victory over challenger Barack Obama in the New Hampshire Democratic primary.

Compare Candidates | Slideshow | Newsletter | CNN Coverage

Clinton's victory capped a comeback from last week's third-place finish in the Iowa caucuses and raised the possibility of a long battle for the party nomination between the most viable black candidate in history and the former first lady, seeking to become the first woman to occupy the Oval Office.

"I come tonight with a very, very full heart," Clinton told her supporters. "I want especially to thank New Hampshire. Over the last week, I listened to you, and in the process, I found my own voice."

She was accompanied by her husband and daughter as she vowed to give America the "kind of comeback" that New Hampshire has given her, following her upset win.

"We came back tonight because you spoke loudly and clearly," Clinton said. "You want this campaign to be about you, because there is so much at stake for our country. Now together, let's give America the kind of comeback that New Hampshire has just given me."

With votes counted from 86 percent of the state's precincts, Clinton had 39 percent of the vote compared to 37 percent for Obama.

"I am stilled fired up," Obama told supporters Tuesday night as he congratulated Clinton on her victory at about 10:50 p.m. EST. "All the candidates in this race have good ideas and all are patriots who serve this country honorably,"

"There's something happening when Americans who are young in age and in spirit, who've never participated in politics before, turn but in numbers we have never seen because they know in their hearts that this time must be different."

Former Sen. John Edwards of North Carolina trailed with 17 percent and conceded his loss at about 10:15 p.m. EST.

He said he will continue his campaign across the country to give voice to Americans who he says are not being heard, especially people with no health care coverage, no jobs or no homes.

McCain Bounces Back

On the Republican side, McCain had 37 percent of the vote, Romney had 32 and Huckabee 12. Former New York Mayor Rudy Giuliani had 9 percent and Texas Rep. Ron Paul 8.

"We showed the people of this country what a real comeback looks like," McCain said as he savored his triumph. "We're going to move on to Michigan and South Carolina and win the nomination."

McCain rode a wave of support from independent voters to defeat former Gov. Mitt Romney of Massachusetts, a showing that reprised his victory in the traditional first-in-the-nation primary in 2000.

"I just talked to the people of New Hampshire," McCain said. "I talked about the country we love, the many challenges we face together, and the great promise that is ours to achieve.

"Tonight, we have taken a step, but only the first step toward repairing the broken politics of the past and restoring the trust of the American people in their government."

It was a bitter blow for Romney, who spent millions of dollars of his own money in hopes of winning the kickoff Iowa caucuses and the first primary -- and finished second in both.

"We thought we knew New Hampshire," Romney said in his concession speech. "Now we really know New Hampshire."

Former Arkansas Gov. Mike Huckabee, who won the Iowa GOP caucuses last week, ran third in the Republican race in New Hampshire.

Clinton Bracing For Defeat

Clinton, who finished third in Iowa, mounted an unexpectedly stiff challenge to Obama in the nation's first primary. Interviews with voters leaving their polling places showed she was winning handily among registered Democrats, while her rival led her by an even larger margin among independents.

Clinton's performance, based on the early returns, surprised even her own inner circle.

In the hours leading up to the poll closing, her closest advisers had appeared to be bracing for a second defeat at the hands of Obama.

Officials said her aides were considering whether to effectively concede the next two contests -- caucuses in Nevada on Jan. 19 and a South Carolina primary a week later -- and instead try to regroup in time for a 22-state round of contests on Feb. 5.

These officials also said a campaign shake-up was in the works, with longtime Clinton confidante Maggie Williams poised to come aboard to help sharpen the former first lady's message. Other personnel additions are expected, according to these officials, who spoke on condition of anonymity while discussing strategy.

Obama, who won the leadoff Iowa caucuses last week, looked for an endorsement from the powerful Culinary Workers union in Nevada in the days ahead. South Carolina's Democratic electorate is heavily black and likely to go for the most viable black presidential candidate in history.

The Republican race turns next to Michigan, where McCain and Romney already are advertising on television, and where both men planned appearances on Wednesday. Huckabee also was expected to campaign in the state.

Link: Local N.H. Coverage

Video Profiles:

Profile: Hillary Clinton
Profile: John Edwards
Profile: Rudolph Giuliani
Profile: Mike Gravel
Profile: Mike Huckabee
Profile: Duncan Hunter
Profile: Dennis Kucinich
Profile: John McCain
Profile: Barack Obama
Profile: Ron Paul
Profile: Bill Richardson
Profile: Mitt Romney
Profile: Fred Thompson