"To everyone who turned out in every corner of Nevada with determination and heart: This is your win. Thank you," Clinton tweeted, shortly after media reports projected her victory.
With four-fifths of the votes counted, Clinton was at 52.2 percent while rival Bernie Sanders, was at 47.7 percent.
"We won the Nevada caucuses," she wrote in an email to her supporters.
"The choice in this primary might be tough for some, because the truth is, Senator Sanders and I agree on a basic premise: Wall Street, big banks, drug companies, and the like all have too much power and influence in our country," she said.
"Americans are right to be angry. These injustices demand action from all of us," Clinton said.
Sanders telephoned Clinton to congratulate her on the Nevada victory.
"I just spoke to Secretary Clinton and congratulated her on her victory here in Nevada. I am very proud of the campaign we ran. Five weeks ago we were 25 points behind and we ended up in a very close election. And we probably will leave Nevada with a solid share of the delegates," Sanders said.
"I am also proud of the fact that we have brought many working people and young people into the political process and believe that we have the wind at our back as we head toward Super Tuesday," he added.
Clinton's victory in Nevada comes after her narrow win in Iowa and a convincing 22-point loss to Sanders in New Hampshire.
The contest moves next to South Carolina, where Democrats vote on February 27, and then to other states across the country.
In a message to his supporters, Sanders highlighted the positives from the results, saying that the close finish in a state which was "tailor-made" for the Clinton campaign was a message to the political and financial establishment.
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