Hillary Clinton can breathe a huge sigh of relief.

Clinton has won the Nevada Democratic caucus. That's something that was expected for months — but it was suddenly thrown into doubt in the past couple of weeks, as Bernie Sanders appeared to surge in Nevada after a lopsided victory in the New Hampshire primary.

Clinton's victory sets her back on track before next week's South Carolina primary, where she has a commanding lead in recent polls. And it validates the Clinton campaign's theory of the race: that Sanders's appeal might be strong in largely white states, but Clinton is the candidate of the Democrats' nonwhite base.

Clinton is likely to win only a couple more delegates out of the state than Sanders, thanks to Nevada's model of assigning delegates regionally. But she doesn't have to worry about delegate math just yet, because she's just won an important victory that makes clear she's still the frontrunner in this campaign.

It only gets easier from here

Clinton was long thought to be the Democrats' inevitable nominee, but her performance in the first two states to vote fell far short of what she might have hoped for. She barely managed to pull out a tie with Sanders in Iowa and lost badly to him in New Hampshire, and national polls in the past week have been tightening.

So Clinton really needed a decisive win. She wanted to prove she could fight off the Sanders surge and give her campaign some sense of momentum before South Carolina and the first multi-state "Super Tuesday" primary on March 1.

And that's just what she ended up getting. The Nevada results were the first test of how real Sanders's momentum was — in other words, how well he would be able to use his early victories as an opportunity to appeal to voters who hadn't been following the race closely for months.

In the end, then, the Nevada results provide ammunition for the Clinton campaign's argument that Sanders's early strength is a fluke of rural white states where he's camped out for months — and that it wouldn't easily translate to the rest of the country.

It's possible that the Clinton campaign didn't have much to worry about in Nevada at all, and recent polls showing a tied race were flukes (Nevada is notoriously difficult to poll). Or it's possible the Clinton campaign's efforts to pull out all the stops in the last days before the caucuses worked, and managed to get enough supporters to the polls to fight off a Sanders surge.

Either way, the Clinton campaign has demonstrated that it does in fact know what it is doing — and Sanders will have to find another opportunity to show that he's broadening his appeal.