( CNN ) -- Solid support from registered Democrats and women in New Hampshire were crucial Tuesday as Sen. Hillary Clinton rebounded from her third-place finish in last week 's Iowa caucuses . Sen. Hillary Clinton has spent the past few days saying she has the experience to change Washington . She narrowly defeated Sen. Barack Obama in the New Hampshire primary , with 39 percent of the vote to Obama 's 37 . `` Last week , I listened to you , and in the process I found my own voice , '' the New York senator said after her victory . `` Now let 's give America the kind of comeback that New Hampshire has just given me . '' Forty-three percent of self-styled independents said they voted for Obama , and 31 percent said they backed Clinton . Independents made up 43 percent of all voters polled . Addressing his roaring supporters after the race was called , Obama congratulated Clinton . But he was a candidate determined to draw a distinction between Clinton and himself . `` But the reason our campaign has always been different , the reason we began this improbable journey almost a year ago , is because it 's not just about what I will do as president , '' he said . `` It is also about what you , the people who love this country , the citizens of the United States of America , can do to change it . That 's what this election is all about . '' But Clinton was ahead of Obama 45 percent to 34 percent among those who said they were registered Democrats . Those voters made up a majority -- 54 percent -- of all respondents . Clinton also claimed the majority of women 's votes , according to the polling . That 's in contrast to last week 's Iowa caucuses , in which Obama surprised observers by stealing the female vote from Clinton . Analysts say that shift among female voters was crucial to the Clinton turnaround . `` If I had a single word , the word would be 'women , ' `` said CNN political analyst Bill Schneider . `` She got the women back . '' And Schneider said the support of union voters that put Clinton over the top . `` Union voters have her a 10 point lead , '' he said . CNN projected former Sen. John Edwards to finish third . College graduates , who made up 29 percent of the electorate , opted narrowly for Clinton -- 38 percent to Obama 's 37 percent , according to the polling . Those polled who called themselves very liberal , and moderate , went with Clinton over Obama -- although by less than 2 percentage points in each -- and those who said they are somewhat liberal were evenly split . Pundits also were citing the role of former President Bill Clinton in helping his wife recover from what pre-primary polls were suggesting was a deficit of 9 percentage points to Obama in New Hampshire . The former president spent Tuesday in Hanover -- home to Dartmouth College -- where Obama had been expected to win handily . `` They dispatched him to the area that Obama was surging , '' said CNN analyst Donna Brazille , who managed former Vice President Al Gore 's campaign in 2000 . `` I think it had the effect of tamping down Obama support and giving Senator Clinton a real reason to come back in this race . '' New Hampshire was considered crucial to Clinton 's campaign . If Obama had been able to sweep Iowa and New Hampshire -- after months of Clinton being considered the front-runner among Democrats -- it could have given him powerful momentum going into future primaries . `` Age is also playing a big factor -- older voters are overwhelmingly outnumbering younger voters -- a proportion that is clearly benefiting Clinton , '' Schneider said . `` Sixty-seven percent of Democratic primary voters are over the age of 40 , and they are breaking heavily for Clinton over Obama . '' Over the past several days , Clinton has trumpeted her experience , saying that she has delivered change as both first lady and as a senator . After losing to Obama in last week 's Iowa caucuses , it was unclear whether she could overcome what appeared to be Obama 's ability to electrify American voters who had previously taken a sour and skeptical view of politicians and the political process . The duel between the Obama and Clinton campaigns grew especially testy Monday and Tuesday . She said she had more experience than he , and was therefore more qualified . He accused her of representing the status quo of Washington . And on the eve of the New Hampshire primary , Bill Clinton criticized the media for not pressing Obama more fully on Iraq , and accused the Illinois senator of shifting his position to reflect changing attitudes about the war in Iraq . Then , there was an issue unto itself -- Hillary Clinton 's almost-tears . Clinton 's eyes welled up this week while responding to a voter 's question about her health and appearance . Pundits and voters alike questioned whether Clinton 's emotions were sincere or faked as part of some strategy to diminish criticism that she is too steely , too cold . In front of the crowd of mostly female New Hampshire voters , an admittedly fatigued Clinton responded to a question by saying : `` This is very personal for me , it 's not just political , it 's [ that ] I see what 's happening , we have to reverse it . '' Her voice broke , and she was then applauded by the crowd . Polls indicated the show of emotions fared well with male voters , according to CNN 's John King , but turned off some female voters . Edwards was followed in votes by New Mexico Gov . Bill Richardson and Ohio Rep. Dennis Kucinich . E-mail to a friend .
Sen. Barack Obama has electrified younger voters . Sen. Hillary Clinton has maintained favor with voters older than 40 . CNN has projected Sen. John Edwards will finish in third place .