Clinton won at least 16 of the 28 delegates at stake in West Virginia, to seven for Obama, with five more to be allocated.
Obama would still retain his lead in the overall delegate count.
Clinton campaigned heavily in West Virginia and had been strongly favoured to win there.
'Race not over'
Clinton vowed to keep fighting until the Democratic voting ends on June 3 despite her dwindling prospects and a mounting campaign debt.
"I am more determined than ever to carry on this campaign until everyone has had a chance to make their voices heard," Clinton told a victory celebration in Charleston, West Virginia.
"This race isn't over yet. Neither of us has the total delegates it takes to win," the New York senator and former first lady said, adding: "We are in the home stretch."
Clinton, whose campaign is at least $20 million in debt, appealed for money to keep her White House bid alive.
"I'm asking people to think hard about where we are in this election, about how we will win in November," she said, noting her strength in big states like Ohio and Pennsylvania that are critical in a presidential election.
She capitalised on two factors that consistently have helped in her struggle to win the Democratic nomination - a nearly all-white population and the low number of residents with tertiary education.
Whites without college degrees were nearly two-thirds of voters, according to early results from exit polls.
Of that group, about three quarters supported her, one of her best performances of the year with them.
Clinton won at least 15 of the delegates at stake in West Virginia, with 13 more to be allocated.
Clinton also looks set to win Kentucky next week, but the numbers look overwhelmingly in Obama's favour.
Obama conceded defeat in advance in the state, looking ahead to the fall campaign against Republican John McCain.
Obama now has 1,875.5 delegates, to 1,712 for Clinton, out of 2,025 needed to clinch the nomination at the party convention in Denver this summer.
The first-term Illinois senator has already picked up 30 superdelegates in the week since he routed Clinton in North Carolina and narrowly lost Indiana.
Clinton added two superdelegates in the same period.
Superdelegates are the nearly 800 party leaders and elected officials who may vote for whomever they choose at the party's nominating convention regardless of the state primary or caucus results.
Four more superdelegates endorsed Obama on Tuesday.
"This race, I believe, is over," said Roy Romer, a former Democratic National Committee chairman and one of the superdelegates who endorsed Obama.