Clinton beat out Obama, who rode a wave of momentum from the Iowa caucus into the Granite State, winning narrowly by only a few percentage points there.
Clinton's historic victory in New Hampshire makes her the first woman, and first former first lady, to win the Granite State primary.
This morning, Clinton told "Good Morning America's" Robin Roberts she had a good feeling about her chances yesterday and didn't pay attention to the polls.
"The voters of New Hampshire are fiercely independent, and they give you the once over," Clinton told Roberts.
Never thought to be a major factor in New Hampshire, former North Carolina Sen. John Edwards came in a distant third in the state, garnering 17 percent of the vote, and will now focus his limited resources on South Carolina, where he won in 2004.
In her victory speech Tuesday night, Clinton told a crowd of supporters in Manchester, "Over the last week, I have listened to you, and in the process I found my own voice."
This morning, Clinton said her much-talked-about emotional moment Monday speaking to a group of mostly women voters may have given her credibility with older women, who turned out in high numbers for her. "I think it could well have been," she said.
Clinton had been responding to a voter who asked her how she does it.
"I've asked that question to people in so many settings for so many years," Clinton told Roberts, "and we're finally understanding what that's about."
"I've always considered myself a servant-leader," Clinton said. "I felt that I could finally convey that to people, and I felt that I could connect that in a profoundly personal way."
However, the woman who sparked the emotional response from Clinton admitted Wednesday that she voted for Obama.
"I went to see Hillary. I was undecided, and I was moved by her response to me," Marianne Pernold Young, 64, a freelance photographer from Portsmouth, told ABC News in a telephone interview.
"We saw 10 seconds of Hillary, the caring woman," she said. "But then when she turned away from me, I noticed that she stiffened up and took on that political posture again," she said. "And the woman that I noticed for 10 seconds was gone."
With his numbers among young voters and women in New Hampshire not what they were in Iowa, Obama said this morning on "GMA" that his campaign was "working it hard" in what he deemed "a close contest."
Obama tried to speculate on what led to his second-place finish in the Granite State.
"College students aren't back in school," the Illinois senator offered. "Sen. Clinton ran well among women in New Hampshire."
And what about former President Clinton's Monday comments that Obama's candidacy was a "big fairy tale?"
"President Clinton is passionate about his wife and wants to see her win," Obama said. "And during the course of this week said some things that distorted my record."
In his post-primary interview with Robin Roberts, Obama shifted focus to the larger race, saying that "voters are excited about the Democratic field. We're attracting a lot of independents and a lot of Republicans to vote Democratic this year." Obama said that people who thought they knew what voters were thinking was "fooling" themselves.