But Obama, who would be the first black U.S. president, retains a nearly insurmountable advantage in delegates who will select the nominee at the party convention in August. West Virginia had only 28 delegates at stake.
Clinton, a New York senator and former first lady, has vowed to keep fighting despite her dwindling prospects and a mounting campaign debt.
"I wouldn't be doing this if I didn't believe that I could be the best president for West Virginia and America and that I was the stronger candidate to take on John McCain in the fall," she said at a rally in Logan, West Virginia on Monday.
The MSNBC delegate count gives Obama 1,874 delegates to Clinton's 1,702, leaving him 151 short of the 2,025 needed to clinch the nomination. Neither candidate can win without help from superdelegates -- nearly 800 party officials who are free to back any candidate.
Obama has been gaining ground among superdelegates for weeks and picked up four more on Tuesday. He now has a narrow lead over Clinton among superdelegates with less than 250 still uncommitted.
A newly minted Obama supporter, former Colorado Gov. Roy Romer, said on Monday it was impossible for Clinton to catch Obama. "The math is controlling. This race, I believe, is over," he said on a conference call sponsored by the Obama campaign.
Exit polls showed Obama picked up more than one-quarter of the white vote in West Virginia, which has a very small black population. Two of every 10 white voters said race was a factor in their vote, and only a third of those said they would support Obama against McCain.
About half of West Virginia voters said the Illinois senator shared the views of the Rev. Jeremiah Wright, his controversial former pastor.
Obama was already looking to November. He visited the general election battleground of Missouri, with stops planned in Michigan on Wednesday and in Florida next week.
After West Virginia, five more contests remain in the Democratic nominating battle with a combined 189 delegates at stake. Oregon and Kentucky vote on May 20, while Puerto Rico votes on June 1 and Montana and South Dakota vote on June 3.